Forces at Play

Forces at Play is a cellular automaton I created in 2022. (If you don’t know what a cellular automaton is, you can think of it as a simple sandbox game where you build machines out of basic units called “cells”.) The source code is available on Github.

Forces at Play was inspired by a game called Cell Machine by Sam Hogan. In Cell Machine, you only have a fixed number of cells to work with, and you must arrange them to accomplish a specific goal. However, Forces at Play is more open-ended; you can place as many cells as you want, and you can do whatever you want with them. I also added two types of cell that don’t exist in Cell Machine: shifters and destroyers.

Cell types

There are nine kinds of cell:

  • Empty (white square)

  • Pusher (blue square with arrow)
    Moves in the direction of the arrow, pushing the cells in front of it, unless blocked by a wall or a board.

  • Box (black square with white square inside it)
    Doesn’t do anything on its own, but can be moved by other cells.

  • Wall (solid black square)
    Cannot be moved by other cells.

  • Board (black square with parallel lines)
    Boards with horizontal lines can move horizontally but not vertically; boards with vertical lines can move vertically but not horizontally.

  • Destroyer (red square with parallel lines)
    Adjacent cells in the direction of the lines are safe; adjacent cells perpendicular to the lines are deleted.

  • Shifter (purple square with arrow)
    Similar to the pusher, but doesn’t move itself, only the cells in front of it.

  • Rotator (green square with arc)
    Rotates the adjacent cells. There are two types of rotator: the one with a “C” rotates things counterclockwise, and the one with a “Ɔ” rotates things clockwise.

  • Generator (yellow square with arrow)
    Creates copies of the cell behind it.


  • Click: select cell
  • Click and drag: select region
  • Arrow keys: move selected region
  • W: create wall
  • E: create box
  • F: create/edit board
  • D: create/edit destroyer
  • R: create/edit rotator
  • Q: create/edit pusher
  • S: create/edit shifter
  • A: create/edit generator
  • Backspace or tab: delete region
  • Space: start/stop automaton
  • Digits 1-5: change animation speed (1 is slowest, 5 is fastest)

Copy and paste

You can copy and cut regions of the grid using ctrl-C and ctrl-X respectively. Use ctrl-V to paste the copied pattern.

When you copy a pattern, a text representation of that pattern is saved to your device’s clipboard. This allows you to save and import patterns by converting them into text and vice versa. For example, try pasting the following text onto the canvas: Pzerzfr.

Pattern catalogue


A spaceship is a pattern that moves across the screen in a regular manner. Spaceships are classified by their speed, measured as a fraction of the “speed of light” (the speed at which pushers move, denoted by the letter c). For example, a spaceship that moves forward by two cells every five steps is said to have a speed of 2c/5.

c P
4c/5 Perz
3c/4 Pzr
c/2 Pz
2c/5 Pzerz
c/3 PFrz
c/4 Pzrf
c/5 Pzerzfr
c/6, c/8, c/10, … PFre1zZ1z
steamboat PFr
destroyer ship PfrGD
growing spaceship PzeG
shuttle ship PFR;3PR


A stacker is a pattern that uses a generator to create a box every N generations. The number N is called the “period” of the stacker.

p1 eG
p2 S;eG;;s
p3 2S;2eG;Z2z;1s
p4 2S;Z1eG;3z;1s
p5 z;;r;eG;s
p6 1w;w;1rQ;2eG;2s;2w
p7 1r;;w;1rQ;2eG;2s;2w
p8, p10, p12, … 2r;;r;2rQ;3eG;3s;3w
p9, p11, p13, … 2z;;2r;;Z;2rQ;3eG;3s;3w


A gun is a pattern that creates a pusher every N generations. If the pushers always go in the same direction, the number N is called the “period”. If the pushers alternate direction, the number N is called the “mod” or the “half-period”. Guns that output more complex spaceships, rather than just pushers, can also be constructed.

p1 Pw;A;P
p2 Pw;A;;w
p3 1S;2w;1Pzw;sA
p4 2Pw;wrAw
p5, p7, p9, … 2R;R;1P1Rw;1A
p6, p10, p12, … wR;2P1Rw;2A
p8 R;P;A
m1 wZPp1zw;3A;3P
m2 1w;1r;wPw;1A;;1w
m3 1S3S;;1Z1p1f;rfRArzR;1swPws
m4, m6, m8, … 2S1S;;wr1P1Rw;3A
m5 2S1S;;r2P2R;2rAR;;2R1r
m7, m9, m11, … RDr;;rAR;1P;1A
random gun 2Pwp;wRAwArw
longship gun R;P1ee;A1AA;;2ww
c/2 gun R;P;A1w;2z;2aS;wZ;3zz;2s
steamboat gun R3w;P1F1r;A1A1a;;2w1w


A rake is a moving gun, or a spaceship that shoots pushers. Rakes which shoot backward are called “backrakes”.

c/2 rake 1Pz;PAz;;PFz
c/2 backrake 1Pz;PAz;P1PFr
c/4 rake 5Pzrf;PzrfA
double barrel c/4 rake 5Pzrf;PZrfA
c/4 backrake 2Pfrez;PAFrez
c/4 side rake 2Pfrez;PAeFrez


all-purpose reflector 17w;17R;17Sr;Pfr3Pz3Pee4rw
boardship reflector 6r;;PF;5sr1R;5R
destroyer turner 1R;rGr;2d1s1s
strange puffer Pfr;PA
self-destruct P3D2d;5r
pusher-to-box converter 7S;P1P5d;7G;6e;7s
box-to-pusher converter z;;r5S;eG5d;s5G;5Q;5ws
board reflector 1z;;1r;1e;FG5d;1s4AS;5Z;6r1R
teleporter 4D;P4eeeeeS1z;11e;11e;11e;11e;11e;11Z6Pw;12eeeeeA1z;11s
OR gate 5Q;;;;4R;P;4r
AND gate 6Q;;;;5Z;P5d;6e;6r;;6Z
half adder 8Q;;;;;9G;7Z;8d;P5f1e3A;4As2r3e1d;3r8e;8Z3e;4R4R2d;;9r1A1d;;11R
4-bit binary counter r1R;;;;;;2R1r;2P6er;2A6AAR14r1D1D1D;9er;9wwr1d2d2d2d