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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Journal of consciousness studies 8 (2001) 3-34.
[26] C. Jemmali</journal-title>
      </journal-title-group>
      <issn pub-type="ppub">2153-0866</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1007/978-3-030-14687-0_5</article-id>
      <title-group>
        <article-title>PCG-SAF: Procedural Content Generation via Self-Assembling Figures for Tabletop Games</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Fiona Shyne</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Seth Cooper</string-name>
        </contrib>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>5204</volume>
      <fpage>44</fpage>
      <lpage>54</lpage>
      <abstract>
        <p>Tangibility within tabletop games is an important factor to many gamers. Commercial games can include methods to procedurally generate tangible content using only analog components, however these are limited in their capability: they usually require manual assembly. Within nature, we find many systems that are able to “selfassemble,” using the physical properties of components to arrange themselves in response to undirected motion. In this work, we use this process of self-assembly to procedurally generate tangible game figures: miniatures and dice. We iteratively designed bases (self-assembly connection points) that are selective, attractive, and adhesive. We qualitatively evaluated this design, and found that they are successfully able to self-assemble, although improvements can still be made. We have complied our work into a toolkit that hobbyists with the necessary materials can use to produce self-assembling game elements.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;procedural content generation</kwd>
        <kwd>self-assembly</kwd>
        <kwd>tabletop games</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        time global structures form. Researchers in macro self-assembly have taken inspiration from chemistry,
and propose that self-assembly can be a construction method for man-made structures, for example
components of micro electronics [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>This project presents a method for creating self-assembling figures for tabletop games (see Figure 1).
We have taken models of game figures, specifically dice and character miniatures, and broken them into
smaller fragments that can be self-assembled in a mix-and-match manner when shaken. Each fragment
is given one or more binding sites, which we refer to as “bases”, that selects and is attracted to specific
other bases. By having multiple candidates for each binding site, the final form of each figure is randomly
determined by the motion of the player shaking a jar. This process is analogous to computational
methods for procedural content generation, for example constructive methods that randomly select
combinations of elements. We further demonstrate that self-assembly can not only result in procedurally
generated content but procedurally generated generators, in the form of self-assembling dice.</p>
      <p>In this paper we present a toolkit for designers to create their own self-assembling figures for tabletop
games. Further, we demonstrate some of the gameplay that becomes possible with self-assembling
ifgures, through the creation of a proof-of-concept game “Rattle, Roll, Rumble.” We evaluate the
feasibility of our approach, through shake tests across several conditions. We demonstrate that these
fragments are successfully able to self-assemble, although the outcomes are sometimes inconsistent.
Self-assembly not only provides a fun, novel interaction method for tangible figures, it opens the door
to mechanical opportunities for completely analog games. While our example game already shows new
opportunities, we believe we are just on the cusp of discovering what is possible when game designers
are given self-assembly as a medium for procedural content generation.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <sec id="sec-2-1">
        <title>2.1. Tangible Game Design</title>
        <p>
          Tabletop gaming provides a unique experience that cannot be completely replicated in digital
entertainment. Rogerson et al. [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] interviewed tabletop gamers and found several themes for what draws
players into tabletop gaming, one of which was the materiality of the medium itself. All factors of
the material quality of the game were mentioned, from the design of the box and the components
to the specific smell new board game pieces have. Tabletop gaming has specific appeal to diferent
populations. Al Mahmud et al. [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] describes how senior citizens are more likely to be drawn to tabletop
games, as the themes and mechanics are similar to what they are familiar with and the interaction
method is more appreciable. For many, the collection of physical components is a significant part
of their hobby. Darzentas et al. [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ] conducted an ethnographic study of miniature collectors within
the genre of war games (such as Warhammer). To these individuals, the value of the miniatures goes
beyond the game, where the collection, customization, and display of miniatures are equally important.
Physical components are often more then simple vessels for gameplay, but can become beloved objects
admired for their physical properties, aesthetics, or associated with previous gameplay experiences.
        </p>
        <p>
          Developments in fabrication technology has the potential to expand what is possible for tangible
game play. Bhaduri et al. [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] explores the possibility space for how 3D printers can be incorporated into
gameplay. They propose that 3D printer can be utilized in a variety of ways including: creating objects
that react to player input, revealing hidden objects, creating records of gameplay, or generating map tiles
during gameplay. Stemasov et al. [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] explores how the act of creation, through 3D printing pens, can be
incorporated into game play. Their project presents a Tabletop roleplaying game, where players craft
their weapons, computational system assess these crafts, and a laser cutter can move or destroy tangible
components of the game. Our work explores a new possibility space for how fabrication technology
can enhance tangible gameplay. Our 3D printable components allow for the physical structure of
gamepieces to be randomly constructed through shaking. This allows for diferent configurations to be
randomly assigned during gameplay only using tangible components.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Procedural Content in Tabletop Games</title>
        <p>
          Procedural content generation (PCG) describes how content in games can be created through algorithmic
processes. Computational PCG has been used to create a wide variety of content, both for digital and
tabletop games. Shyne and Cooper [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] preformed a literature review on computational tool for tabletop
role playing games. This work found that PCG has been used to generate a variety of content for
tabletop games, including narrative, maps, dungeons, and even taking the place of a game manager
(GM). However, what has been explored in a completely analog capacity has been less explored.
        </p>
        <p>
          Analog means of procedural generation have a history predating their computational counterparts.
Smith [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ] describes how tabletop games directed randomness to create content, before computer were
able to. They describe two methods they use to accomplish this: modular components (such as map
tiles) that fit together, and randomly driven algorithmic design. Guzdial et al. [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ] further describes
tabletop role-playing games as PCG systems, and discusses how we can use strategies in these games to
inform computational systems. Brown and Scirea [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] describes a framework for how tabletop games
implement PCG methods. These methods includes: random lookup tables where dice rolls determine
which element is chosen, construction of maps using tiles, and procedures that determine turn-order
or enemy actions. We can see these methods in a variety of modern tabletop games. Dungeons and
Dragons [14], presents a series of lookup tables to generate randomized combat encounters along with
rules for randomized turn order. Several games, including Catan [15], Carcassonne [16], and Heroscape
[17], all include configurable map tiles where the players use a procedural process to construct the game
map itself. While these techniques employ algorithmic and randomized processes, the construction of
structures still have to implemented by the players. In this work we present a new method for PCG in
tabletop games, where the structure is assembled automatically and randomly, using the randomized
motions created through shaking.
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Self-Assembly</title>
        <p>
          Self-assembly describes a wide variety of processes for how individual components automatically
assemble into structures, from the smallest of molecules to entire solar systems. Whitesides and
Grzybowski [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] describes self-assembly to systems with the following features: systems are made
up of pre-existing components, the process is reversible, and the process can be controlled through
the design of its components. In a self-assembling system, information is encoded onto individual
components, which are able to move freely through the introduction of energy, and components are
either attracted to or repelled from each other through their individuals properties. In a micro context,
components are often attracted to each other through non-covalent or weak covalent interactions, such
as van der Waals bonds. On a macro scale, components are attracted using a variety of forces including
magnetic and gravitational attraction. Soute et al. [18] describes how the properties of self assembly,
including self-repair, self-replication, and growing and mutating new structures, are useful to large
scale construction.
        </p>
        <p>Self-assembling systems share a lot of similarity with computational techniques. Winslow [19],
demonstrated that a specific model for self-assembly, staged self-assembly, can be represented with up
to a logarithmic increase in size from polynomial context-free grammars. Klavins [20] describes how
you can represent a self-assembling system using graph grammars, which can be used to reason about
what the final form of a self-assembling system.</p>
        <p>Previous self-assembling systems in the centimeter scales have used a variety of techniques. Common
among these techniques is the use of magnets to attract and repel pieces. Majumder and Reif [21]
provides a framework for 2D tiles that self-assemble, where the polarity of the magnets on each side of
the tile determines which other tiles it attracts. Jílek et al. [22] implements a strategy similar to this,
with 3D printed pieces that contain slots for inserting magnets into the sides. They also curve the edges
of each piece to assisted with “guiding” adjacent components into the right position. However, this
manufacturing process can be tedious and require a substantial amount of individual magnets to define
diferent interactions. Nisser et al. [23] addresses these concerns with their design of magnetic cubes
that can be “programmed” using a specialized machine that can set the polarity of magnets. On each
side of these cubes is a magnetic sheet, where the polarity each individual “pixel” can be set and edited
by the machine. While this process provides existing opportunities, it requires access to specialized
and expensive equipment that most people, our lab included, do not have access to. Hacohen et al.
[24] proposes another method for selection. In this work, each piece contains only one magnet, and
selection is determined by having extruding cones (pegs), or indentations (holes). Our work uses this
approach as a basis, iterating on this design, to create a toolkit that is accessible to hobbyists with
moderate technical experience.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Design Process</title>
      <sec id="sec-3-1">
        <title>3.1. Design Goals</title>
        <p>Here we describe our design goals and iterative prototyping process, along with the final product and
an example game created with these figures.</p>
        <p>The goal of this project was to create a system to produce gameplay figures (i.e. minatures and dice)
that self-assemble, in a short time frame, when being shaken by a human player in a jar. We found
no existing models that fit this goal. Existing work, 1) did not have any publicly accessible models,
and 2) looked at figures that self-assemble when machine generated motion is applied and only fully
assemble after several minutes. This was not ideal for our goal, as we wanted players to explicitly to
participate in the self-assembly process. We did find existing models, on the Thingiverse 1 website,
for self-assembling components that were meant to be shaken. However, these models only allow for
one repeating model to be present in the existing structure. For example one model, is supposed to
represent a virus and consists of 12 identical pieces that form a dodecagon. The problem with this
model is there is no method of selection, all pieces are attracted to each other.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Problem Definition</title>
        <p>With our goal in mind we developed a set of terminology to describe diferent components of the project
(see Figure 1 for labels). In our project a figure, is a collection of self-assembling fragments that are fully
assembled into their final form. Each fragment contains one or more bases, which is what the makes
the fragments attracted to other fragments. Bases have cues, that determine which other bases it can
connect to. Cues are either indentations, called holes, or outward faces cones, called pegs. Each base has
a set number of positions of which cues are placed. The length and position of each cue, determine
which other base(s) it selects. Bases have magnets glued into them that make them attracted to other
bases. Once two bases are attracted to each other if they are compatible (they select each other) they
become connected. The strength of this connection is called its adhesion. The goal of this project is to
design bases that are to be placed on fragments, that have the following properties:
1. High Selection: Bases should only be able to connect with compatible bases, in the correct
orientation. For any base (), it should only be able to select it’s perfect match (′) and not other
base in the set.
2. High Attraction: Bases should be highly attracted to each other, such that when in a moving
environment, it is likely that they end up close enough to become attracted to each other.
3. High Adhesion: Once bases are connected to each other, they should remain connected even
when continuing to be shaken.</p>
        <p>We wanted to make this project completely open source. Currently, we have the files related to
this project on an Open Science Framework project [LINK]. This project has all models produced,
both from prototypes and the final version, along with the printing file (either in ultimaker or gcode
format). Additionally, we have a series of video demonstrating the properties of diferent prototypes.
For the finalized version, we have included a complete guide to modeling, printing, and assembling
the self-assembling fragments. Finally, we have included complete instructions for a example use case
game: “Rattle, Roll, Rumble" about constructing robot armies to take into battle.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Prototypes</title>
        <p>In this section we describe our iterative prototyping process. Developing self-assembling game pieces
was an iterative process of trial and error. We originally started with trying to replicate designs from
previous academic work, and continuously found methods to improve the attraction, adhesion, and
selection of printed pieces. These values were accessed qualitatively. All prototypes are shown in</p>
        <sec id="sec-3-3-1">
          <title>Prototype 1: Replication</title>
          <p>Our first attempt at creating bases was to replicate an approach we found in previous work [ 24]. In
this project, bases have a center shape that either sticks out or is indented. The magnet for the base is
placed in the center of this component, with north facing magnets being placed in bases that stick out
and south facing magnets being placed in bases that are indented. The shape of this center component is
orientation specific (e.g. a pentagon), such that bases are only attracted to each other if the orientation
is correct. They also had diferent center shapes, but we started with implementing only the pentagon
shape. On the outside of the bases, there are several positions for cues. Each cue could take one of
7 lengths out of [−3, −2, −1, 0, 1, 2, 3]. Negative positions refer to hole,
0 is a flat surface, and positive positions are pegs.</p>
          <p>We could not locate the exact models used in this paper, so we started from scratch to replicate this
work. In order to make it easier to modify the work, we used the programming based CAD software,
OpenSCAD 2. This program generates a 3D model from a basic scripting language. This allowed us to
create a simple base program, where one can easily modify the diferent parameters including: number
of cues, the heights of each cue, and dimensions of the base. This first prototype consisted of 5 cues,
with a center hole for one 3 × 1 magnet. To determine the heights of each base in the set, we wrote
a simple program that, through trial and error, returns a set of heights such that each base can only be
selected by its perfect match. Selection is determined by — for each position — if the hole is at least as
deep as the length of the peg in the pair (as long as the pair have alternative polarity). This program
randomly generates height sets and only adds them to final list if they are not selected by any other
base in the set.</p>
          <p>This program and the OpenSCAD file were used to create a set of 3 bases and their perfect matches
(for 6 total bases). To test out the bases, a simple robot model was created on the TinkerCAD 3 software.
This model was broken up into 5 fragments, one head, two arms, a torso, and one pair of legs. The
bases were attached to the robot fragments such that the head can select the top of the torso, the torso
can select an arm on either side of its body, and the legs can select the bottom of the torso. Note that
in this model the arms are interchangeable and use the same base. We printed these fragments at our
university Makerspace, on a Ultimaker S3.</p>
          <p>This first prototype had many flaws. First, the indentation of the center shape was too shallow
to be useful. Orientation was enforced, but through the cues and not the center shape. While this
worked out in our sample set, we made no assumption that bases could be attracted to each other in
diferent orientations in our height generation program. Therefore, it would be easy to accidentally
create a set of bases where one base is attracted to a wrong base at an alterative orientation. Second,
the sole 3 × 1 magnet was not nearly strong enough to attract fragments together. Even if you
placed the fragments together, they would fall apart easily, leading to low adhesion as well. Third, we
printed the legs with the base facing down which lead to fatal printing flaws on the base. From this
we determined that bases should only be printed on their side or facing up. Lastly, the magnets were
extremely dificult to place as the magnet holes were only marginally larger then the magnets themselves.</p>
        </sec>
        <sec id="sec-3-3-2">
          <title>Prototype 2: Increasing Center Height</title>
          <p>Our second prototype addressed many of the problems of the first prototype. We increased the height
of the center component, added a second magnet to each base, and made the magnet holes larger. These
changes, particularly the center height, had an substantial impact on selection and adhesion. Given
the distance between the magnets and face of the fragments, bases were only attracted to each other
if the fragments were in the exact correct orientation. While there was some evidence the fragments
would self correct their position, this was fairly uncommon and manual correct was often needed.
Additionally, the distances between magnets enforced the selection property of the cues. Bases could
2https://openscad.org/
3https://www.tinkercad.com/dashboard
only be connected if the pegs were fully enclosed in the holes. The fragments in this version also had
much higher adhesion. Fragments that were gently placed on each other could sustain light shaking
(compared to previously where even gravity would disconnect fragments). If the fragments are slightly
pressed together, adhesion improved greatly and significant shaking was needed to separate fragments.</p>
          <p>However, bases still had low attraction, despite the additional magnet. Since shaking demonstrated
no attraction, we tested how attracted fragments were by gently dropping them on top of each
other. Fragments could connect when dropped from a few millimeters away, and at least close to
the right orientation. But any further distance, or greater orientation diferences, and the fragments
demonstrated no attraction.</p>
        </sec>
        <sec id="sec-3-3-3">
          <title>Prototype 3: Removing Center</title>
          <p>For the next prototype, we attempted to improve attraction by both removing the center component
and placing 4 magnets on each base. Now, to enforce orientation, we used the polarity of the magnets.
In the “north facing” base, only three of the magnets are north facing with one magnet being south
facing (the “south facing” base is the inverse). With this set up, bases in the wrong orientation can only
be attracted to 2 out of the 4 magnets.</p>
          <p>This new design did have improvements on attraction. We could drop the fragments from a greater
height and still get connections. However, attraction was still not great enough for any self-assembly to
occur when shaken. Without the center shape, orientation was not strictly enforced, and fragments
were attracted to each other even when the bases were wrong. Additionally, the center shape seemed
to have a large efect on adhesion, as without them the pieces could only tolerate very light shaking.</p>
        </sec>
        <sec id="sec-3-3-4">
          <title>Prototype 4: Larger Magnets</title>
          <p>After several prototypes with limited success, we turned back to existing self-assembly work as
inspiration. Instead of looking through academic papers, we search through open source 3D modelling
websites, such as Thingiverse. Available models on these websites had two diferent forms, the first
being a 12 sided polygon to imitate a “virus” 4 and a seaweed like figure 5. Both of these use copies of the
same model and have no selection criteria. However, we decided to print the virus model as inspiration
for this project. This virus model guided us in two ways: first it reminded us of a dice which lead to
us creating a 6 sided dice model for our example game (see Figure 1), and second it used 3 × 1.5
magnets instead of 3 × 1 . While this initially didn’t seem like it would make a big diference, it
ended up having a substantial impact on attraction.</p>
          <p>For the next prototypes, we decided to reduce printing time by just printing the bases and not the
entire robot model. We printed both bases with and without center components, this time with the
larger magnets. While the larger magnet did increase attraction for the base with the center component,
it was still insuficient to successfully self-assemble. The base without a center component, while
having lower selection and adhesion, was substantially more attractive. It was at this point of the
process where we realized that attraction was more important than selection or adhesion for this
project. If we wanted fragments that would quickly self-assemble when being manually shaken, we
would want them to be as attractive as possible. While selection is still important, with the small
number of bases we are testing on, it was not as critical.</p>
        </sec>
        <sec id="sec-3-3-5">
          <title>Prototype 5: Simple Robot</title>
          <p>Once we narrowed down on the base configuration, we continued to test them on the robot
fragments. To make the process easier we started with a two fragment robot: one head fragment and one
combination torso and leg fragment. We also constructed two forms for the robots, an angular body
(called “Kiki”) and a smooth body (called “Boba”), inspired by a famous experiment [25]. These two
forms used the same bases, so a Kiki head could be attached to a Boba body and vice versa. This simpler
ifgure, along with highly attractive bases, were substantially more successful. We were able to get the
4https://www.thingiverse.com/thing:2834219
5https://www.thingiverse.com/thing:5353951
fragments to self assemble when shaken, although it could sometimes take a couple of minutes for the
fragments to assemble.</p>
          <p>With the success of the two part robot, we constructed a three part robot: one head fragment, one
torso fragment, one leg fragment. Like before, we made these pieces for both the Boba and Kiki models.
The head and torso attach with same base ( and ′) as the two-part robots, such that same heads are
compatible between the two and three part robots. The torso and legs attach with a diferent base ( 
and ′).</p>
          <p>It was the through the introduction of the second base pair that we noticed the issues with this new
base configuration. While shaking the three parts robots we noticed the legs (with base ′) becoming
attached to the head (with base ) at certain orientations. The attraction between bases was so high
that fragments could become connected both at the wrong orientation (where only two magnets can
connect), and when a hole is 1 too shallow for the peg.</p>
        </sec>
        <sec id="sec-3-3-6">
          <title>Prototype 6: Minor Revisions</title>
          <p>Since we realized that attraction was very important, instead of fixing selection by lowering attraction
(such as introducing the center shape) we made the following adjustments:
1. Construct cue height sets such that they cannot be selected at incorrect orientations
2. Make the diference between cue heights at least 2 instead of only 1</p>
          <p>While this has some efect on the number of bases that can be in a system, at the scale we were
working with (only a few bases needed) this was not a problem. We modified our cue algorithm to
check for orientation diferences, and we changed our cue heights to [−4, −2, 0, 2, 4].</p>
          <p>With these changes we came to our final design. While they are certainly be improvements to make
in the future, these fragments are highly attractive and adhesive and have adequate selection.</p>
        </sec>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Self-Assembly Toolkit</title>
        <p>Through finalizing our design, we can present a toolkit for creating custom self-assembling figures. The
process follows a series of steps. All materials are available on OSF 6:
1. (OPTIONAL) Construct a cue height set: Using our Python program, generate a list of cue
heights for base pairs. This program works by randomly generating N lists of size M (our bases
uses  = 4). For each list it generates, it checks if the cues could be selected by any other cue
currently in the list, at any orientation. If there are not other bases that could select it, that list is
added. These values are printed out for the user.
2. (OPTIONAL) Construct base models: Using our OpenSCAD program, copy and paste the cue
lists from the python program for each base. This will generate a STL file containing both that
base (on the left) and its perfect match (on the right). The left base will be the north facing base,
and the right will be the south facing base.
3. Create your 3D Model: Using modelling software of choice (we used TinkerCAD), create a
model for your 3D figure.
4. Add bases to your model: You can either use bases that were constructed in steps 1 and 2, or
use the pre-built bases provided in the kit. Start by breaking your model into however many
fragments you desire. At each joint where you want a base, create a hole that is the size of the
base (16 × 16 × 1 ). Then place the base in the hole and merge the objects together.
Do this for all fragments. Make sure that bases are pairs of each other where you want them to
connected.
5. Print the models: If you do not have a 3D printer, check for local Makerspaces in libraries,
universities, or community centers. Alternatively, there are print by demand services that will
ship fragment to you. When printing, make sure you use a fine detail such as a 0.1 layer
height. Also assure that models are orientated such that the bases are facing up or at a 90% angle
(not facing the build plate). We used an Ultimaker S3 and a Prusa M4 using PLA filament, but
other configurations should work.
6. Glue magnets in: Orient a base such that it is facing up. If this is a north facing base, glue (using
super glue) one south facing 3 × 1.5 magnet in the upper   corner. Glue north facing
magnets in the remaining four holes. For a south facing bases, glue one north facing magnet in
the upper ℎ and south facing magnets everywhere else.
7. Shake and play: Place all fragments in a small plastic jar, and shake until fragments are self
assembled. Reference the evaluation section for more detailed shaking information.</p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Proof of concept: Rattle, Roll, Rumble</title>
        <p>To demonstrate the possibilities that emerge with self-assembling figures, we created an example game:
“Rattle, Roll, Rumble.” Full game instructions and materials are available on the OSF project.</p>
        <p>This is a two player game, where each players controls a robot army. At the beginning of the game
both players place a pre-determined amount of robot fragments in a jar and shake the jar for a set time.
After this time, any robot that is fully assembled becomes a part of your army. Each part of the robot
gives you diferent abilities. For example a “Kiki” torso gives you a short and long range attack, while a
“Boba” torso give that robot a mid range attack and a healing ability. Robots also get bonuses based on
the color of the fragment.</p>
        <p>In addition to self-assembling the robot fragments, players also self-assemble the dice they will use in
the game. Each side of the dice has a diferent color, associated with a diferent type of attack/defense.
After assembling robots and dice, the players take turns taking over their robots and trying to defeat the
other robot army. The authors tested Rattle, Roll, Rumble in a small playtest. This playtest demonstrated
the fun potential of self-assembly, particularly the excitement of watching the figures assemble. However,
there are still several flaws, including game design issues including poor balancing and a repetitive
game-loop along with some physical problems, particularly that the dice came apart and had to be
manually re-assembled. We recognized several opportunities for iteration of this game including
using simulations to assist with balancing and incorporating self-assembly throughout the game (as
self-assembly is currently just used in the game set-up).</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Evaluation</title>
      <p>We evaluate how well our fragments self-assemble through a series of tests preformed by the first
author. These tests varied by temperature (i.e. intensity of shakes), duration, and number of copies.
These tests confirm that this is a feasible design for self-assembly, although there is some concern of
fatigue for the user.</p>
      <sec id="sec-4-1">
        <title>4.1. Methodology</title>
        <p>To test how well the figures self assemble, the first author performed 5 trials for each condition. The
fragments were shaking in an transparent 3′′ × 3.5 ′′ jar. During each trial they measured how many
full connections (two fragments coming together correctly), complete figures (all fragments of a figure
become assembled), and partial or false connections. Partial connections are where two matching
fragments connect in the wrong orientation, and false connections are partial connections between two
fragments that do not match. False connections are weaker then partial connections, which are weaker
then full connections.</p>
        <p>Each trial varied by several conditions. The first condition was to test the diferent models we created:
1. Two part robot: robot model with a head and torso fragments
2. Three part robot: robot model with a head, torso, and leg fragments
3. D6 dice: six sided dice with 6 identical fragments</p>
        <p>Next we varied the temperature (how intense the shakes are) between low and high temperature. We
decided to use a loose interpretation for these terms, as this will eventually be given to an end user
who will have to interpret written directions. In the low condition the first author shook the jar just
enough for the fragments to move, but where the the fragments had little vertical movement. In the
high condition the jar was shaken enough for relatively constant movement of the fragments in all
directions. We also varied how long we shook the jar between 30 seconds to 90 seconds, and how many
copies of each fragment were added (1, 2, or 3). Since the dice figures assembled faster, we only tested
these up to 60 seconds.</p>
        <p>Videos and outcomes of all trials are available on Open Science Framework (linked above).</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Results</title>
        <p>The results from the trial are shown in Table ??. Below we talk about the efect of the diferent conditions.</p>
        <sec id="sec-4-2-1">
          <title>Time</title>
          <p>The more time the jar is shaken, the more figures are able to form. Across all robot conditions,
6% of trials were able to form at least one figure in 30 seconds, 25% in 60 seconds, and 32% in 90
seconds. However, increasing the time too much may also have negative efects. In the 90 second trial,
connections would often form and break before the time was up. Also the 90 seconds, especially with
the high temperature, was tiring for the first author to complete.</p>
        </sec>
        <sec id="sec-4-2-2">
          <title>Copies</title>
          <p>Increasing the number of copies also increased the chances of complete figures forming. For trials
with only 1 copy, 10% assembled complete figure compared to 22% for two copies, and 37% for three
copies. There are some issues with increasing the number of copies. The additional fragments can
interfere with the assembly process, either by breaking connections or creating partial and false
connections. These partial and false connections most often break apart quickly, but prevent true
connections from forming for those fragments. These problems are potentially mitigated by having a
larger jar when introducing more copies.</p>
        </sec>
        <sec id="sec-4-2-3">
          <title>Temperature</title>
          <p>For the robot figures, the lower temperature was more successful. In the low temperature 31% of
trials resulted in a completed figure, compared to 14% for high temperature. However, both high
and low temperatures have benefits. In high temperatures, the bases are more likely to interact and
partial or false connections are easier to break. However, bases that do interact are less likely to
connect and connected bases are more likely to break. In contrast, in low temperatures there are less
interactions between fragments, but fragments that do interact are more likely connect and stay connected.</p>
        </sec>
        <sec id="sec-4-2-4">
          <title>Robot Models</title>
          <p>Somewhat unsurprisingly, the 2-part robot had more trials that resulted in complete figures then
the 3-part robot. For the 2-part robot, 32% of trials resulted in complete figures, compared to 13% for
the 3-part robot. That being said, the 3-part robot had more connections, with an average of 0.85
connections per trial compared to 0.4 connections in the 2-part robot. This is slightly more then we
would expect from the fact that the 3-part robot had twice as many bases that could connect.</p>
        </sec>
        <sec id="sec-4-2-5">
          <title>Dice Models</title>
          <p>The dice fragments behaved very diferently from the robot models. The dice, having 8 dice on a
smaller volume space, where highly attractive. This meant that complete figures were assembled at
higher rates, however this also meant there was an increase of partial connections. This was such
a problem that the low temperature was often unable to break away partial connections, leading to
less complete figures. This was even more evident in the 3 copy condition, where the extra fragments
distrusted the assembly process. Overall the dice consistently form at a higher rate, with all trials with
.
p
m
e</p>
          <p>T
low
low
low
high
high
high
low
low
low
high
high
high
low
low
low
high
high
high
.
s
n
n
o
C
l
l
u</p>
          <p>F
.
s
n
n
o
C
l
l
u</p>
          <p>F
high temperatures that ran for at least 60 seconds being able to assemble a complete figure. The high
temperature produced a complete figure at 30 second when 2 copies were present.</p>
        </sec>
        <sec id="sec-4-2-6">
          <title>Usability</title>
          <p>While we did not test this formally, we did consider how usable these fragments are as actual game
fragments. The robot fragments are certainly stable enough to be used, although breakages may occur.
These breakages should be trivial to repair. The dice are able to be rolled without breaking, although
they have to be treated delicately. Harsh throws, or tools like dice towers, would easily break apart the
dice. These breakages might be harder to repair, as it requires the player to remember where each side
goes.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Discussion</title>
      <sec id="sec-5-1">
        <title>5.1. Value of Toolkit</title>
        <p>In this work we present a toolkit for making self-assembling figures for tabletop gaming. This toolkit is
more accessible then previous work in this area. Designers who want to use this system would need
to have some technical knowledge, but don’t need to have extensive CAD or programming language
experience. The assembly process is fairly easy, although it does require some fine motor control and
understanding of magnetism. Further, the materials to make a self-assembling system are relatively
inexpensive. Designers do need access to a 3D printer, but these are becoming increasingly accessible
in home and communities environments. We used an inexpensive variety of 3D printing filament,
along with inexpensive magnets and super glue. Overall this toolkit is approachable to the hobbyist
population.</p>
        <p>The results of our evaluation show that the figures are able to self-assemble. However, we have not
been able to find a condition that consistently results in fully formed figures, especially for the 3-part
robot. This could indicate that improvements need to be made to the system. For example, we could
consider having a single large magnet in the center of the base. This could improve adhesion, along
with reducing the possibility for partial connections at one of the magnets at the edge. We could also
continue to experiment to find the ideal way for the fragments to self assemble. For example we haven’t
yet looked at the way the jar was shaken, nor the size of the jar. It is possible, if not likely, that shaking
for self-assembly is a skill that can be improved overtime. While conducting the experiments, the first
author did notice themselves “trying” to get the fragments to self assemble. Moving the jar such that
the fragments that needed to connect are closer together, or subtle slowing the shaking motion to avoid
connections breaking apart.This level of skill could be undesirable, if the designer wants the outcome to
be completely random, in which case, an opaque jar may help reduce the level of skill. However, the
introduction of shaking skill could be considered an additional game mechanic to learn.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Possibility Space</title>
        <p>We have demonstrated two uses for PCG-SAF: randomly constructed miniatures and dice. In our
example game, we determined mechanics that could be associated with each fragment of the robot.
This means that every self-assembled figure will not only look diferent, but have diferent efects on
gameplay. We had a simple formula for how figures should form, with each having any head, body,
or torso. However, designers could choose to have finer control over this process. For example, a
torso could accept only certain legs or heads. This can be used to ensure that incompatible mechanics
don’t occur. Future designers could also consider figures without set number of pieces in them. For
example, some arms could attach to both the torso and a weapon, while other arms only attach to
the torso. Alternatively, fragments could allow creating structures that range widely in size like the
“seaweed” mentioned above. We noticed several times where fragments could partially connect. This
could either be seen as undesirable, or could be an opportunity to introduce more game mechanics
(e.g. special mechanics for a “two-headed” robot). The self-assembled dice bring further possibility
for not only procedurally generating content, but random generators as well. Board games have long
used customized dice, but this allows for dice to both be specific to a player and be randomly assigned.
Future designers could consider diferent dice sizes, or even experimenting with the physical properties
of the dice such as weighting the sides diferently.</p>
        <p>However, these use cases are only a narrow range of what could be possible with a PCG-SAF
system. Along with figures and dice, designers could consider using self-assembly to construct game
boards, maps, or dungeons. Mechanics that have you drawing from a deck, could be replaced with
self-assembling a figure and interpreting the results. PCG-SAF has a lot of parallels to computational
methods for PCG. Self-assembly could be considered as a type of grammar, which has been used for
PCG previously [26, 27, 28]. One could consider how to translate past work on grammars for PCG into
a PCG-SAF system. Further, PCG-SAF focuses on local interaction, which is similar in concept to PCG
algorithms such as Wave Function Collapse [29]. It seems plausible that a Wave Function Collapse
like algorithm could be implemented using PCG-SAF; possibly in 3D with voxel-like fragments that
assemble into buildings or dungeons. Self-assembly begins to bridge the gap between computational
PCG and completely analog PCG. Further, the range of what all is possible with a PCG-SAF system is
not yet known. By presenting this concept to computer scientists and game designers, we are likely to
discover many existing new opportunities for how to use PCG-SAF.</p>
      </sec>
      <sec id="sec-5-3">
        <title>5.3. Limitations</title>
        <p>As preliminary work, there are several limitations to this project. We only tested our bases with a simple
ifgure, including only two diferent base sets in total. We also introduced rules for a game that could
use these figures, but only conducted a small internal playtest of the game. Further, our evaluation
showed that we were not able to consistently produce full-assembled figures. This is likely to improve
through re-design of the bases, but it may point out some of the inherit limitations with this process.
There is likely a low ceiling for how complex a system can became before it is infeasible in this context,
although we don’t yet know where this ceiling is.</p>
        <p>There are also several ethical considerations to this work. The first is that the process of shaking
can cause irritation or fatigue for players. This risk increases the more complex a system is. There are
also some minor dangers to assembling the pieces. Using super glue, especially in such small spaces,
can cause damages. We have frequently gotten super glue on our hand, which caused slight pain and
discomfort but no serious injuries. Lastly, we want to acknowledge the plastic waste that was produced
in working on this project. While we tried to only print the pieces that we needed, we did produce
plastic waste through failed prototypes, print errors, and support material. The impact of this could
be mitigated through the choice of filament. We used PLA, which is both the easiest to work with
and recyclable and biodegradable [30, 31]. Additionally, PLA doesn’t emit toxins when printing like
material such as ABS. However, future work should consider how to reduce such waste and whether
the artifacts produced are worth the environmental cost of producing them.</p>
      </sec>
      <sec id="sec-5-4">
        <title>5.4. Future Work</title>
        <p>Our evaluation demonstrated that there is still progress to made on the design of the bases. Particularly
it seems there needs to improvements on attraction and adhesion. Along with containing the design
process, future work should consider testing on larger and more complex systems. Understanding the
limits on what can be accomplished is important for considering the design of game mechanics. We
are interested in implementing a simulator to allow more rapid iteration on designs without the use of
additional plastic, as well as exploring diferent materials.</p>
        <p>Future work should also consider how to translate computational PCG methods into PCG-SAF
systems. There seems to be several analogies between computational methods, such as grammars or
Wave Function Collapse, that could be translated into an analog system. Further, game designers could
be consulted to consider how these systems can be utilized. While we introduced our initial ideas
of how to use PCG-SAF systems, board game designers would have a wider idea of what could be
considered. Designers should also be consulted to determine what would be required of these system to
be successfully integrated into tabletop games.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusion</title>
      <p>Despite the many advances in digital entertainment, tabletop games remain a popular medium.
Researchers and designers should continue to investigate how to expand experiences that do not require
digital components. In this work, we presented a method of procedurally generating content for tabletop
games using self-assembling figures. This has the possibility to expand what is possible in tabletop
games. While improvements can still be made, we demonstrate the it is feasible to procedurally construct
ifgures and dice using self-assembly. To promote the development of this work, we provide a toolkit
that allows researcher, designers, and hobbyists to explore this new medium for procedural content
generation.</p>
    </sec>
    <sec id="sec-7">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author(s) used Writefull in order to: Grammar and spelling
check. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s)
full responsibility for the publication’s content.</p>
    </sec>
  </body>
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