A GPU Approach to Conway's Game of Life

Update: In the next article, I extend this program to solving mazes. The demo has also been ported to the Skew programming language.

Conway’s Game of Life is another well-matched workload for GPUs. Here’s the actual WebGL demo if you want to check it out before continuing.

To quickly summarize the rules:

These simple cellular automata rules lead to surprisingly complex, organic patterns. Cells are updated in parallel, so it’s generally implemented using two separate buffers. This makes it a perfect candidate for an OpenGL fragment shader.

Preparing the Textures

The entire simulation state will be stored in a single, 2D texture in GPU memory. Each pixel of the texture represents one Life cell. The texture will have the internal format GL_RGBA. That is, each pixel will have a red, green, blue, and alpha channel. This texture is not drawn directly to the screen, so how exactly these channels are used is mostly unimportant. It’s merely a simulation data structure. This is because I’m using the OpenGL programmable pipeline for general computation. I’m calling this the “front” texture.

Four multi-bit (actual width is up to the GPU) channels seems excessive considering that all I really need is a single bit of state for each cell. However, due to framebuffer completion rules, in order to draw onto this texture it must be GL_RGBA. I could pack more than one cell into one texture pixel, but this would reduce parallelism: the shader will run once per pixel, not once per cell.

Because cells are updated in parallel, this texture can’t be modified in-place. It would overwrite important state. In order to do any real work I need a second texture to store the update. This is the “back” texture. After the update, this back texture will hold the current simulation state, so the names of the front and back texture are swapped. The front texture always holds the current state, with the back texture acting as a workspace.

GOL.prototype.swap = function() {
    var tmp = this.textures.front;
    this.textures.front = this.textures.back;
    this.textures.back = tmp;
    return this;

Here’s how a texture is created and prepared. It’s wrapped in a function/method because I’ll need two identical textures, making two separate calls to this function. All of these settings are required for framebuffer completion (explained later).

GOL.prototype.texture = function() {
    var gl = this.gl;
    var tex = gl.createTexture();
    gl.bindTexture(gl.TEXTURE_2D, tex);
    gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.REPEAT);
    gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.REPEAT);
    gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
    gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
    gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA,
                  this.statesize.x, this.statesize.y,
                  0, gl.RGBA, gl.UNSIGNED_BYTE, null);
    return tex;

A texture wrap of GL_REPEAT means the simulation will be automatically torus-shaped. The interpolation is GL_NEAREST, because I don’t want to interpolate between cell states at all. The final OpenGL call initializes the texture size (this.statesize). This size is different than the size of the display because, again, this is actually a simulation data structure for my purposes.

The null at the end would normally be texture data. I don’t need to supply any data at this point, so this is left blank. Normally this would leave the texture content in an undefined state, but for security purposes, WebGL will automatically ensure that it’s zeroed. Otherwise there’s a chance that sensitive data might leak from another WebGL instance on another page or, worse, from another process using OpenGL. I’ll make a similar call again later with glTexSubImage2D() to fill the texture with initial random state.

In OpenGL ES, and therefore WebGL, wrapped (GL_REPEAT) texture dimensions must be powers of two, i.e. 512x512, 256x1024, etc. Since I want to exploit the built-in texture wrapping, I’ve decided to constrain my simulation state size to powers of two. If I manually did the wrapping in the fragment shader, I could make the simulation state any size I wanted.


A framebuffer is the target of the current glClear(), glDrawArrays(), or glDrawElements(). The user’s display is the default framebuffer. New framebuffers can be created and used as drawing targets in place of the default framebuffer. This is how things are drawn off-screen without effecting the display.

A framebuffer by itself is nothing but an empty frame. It needs a canvas. Other resources are attached in order to make use of it. For the simulation I want to draw onto the back buffer, so I attach this to a framebuffer. If this framebuffer is bound at the time of the draw call, the output goes onto the texture. This is really powerful because this texture can be used as an input for another draw command, which is exactly what I’ll be doing later.

Here’s what making a single step of the simulation looks like.

GOL.prototype.step = function() {
    var gl = this.gl;
    gl.bindFramebuffer(gl.FRAMEBUFFER, this.framebuffers.step);
    gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0,
                            gl.TEXTURE_2D, this.textures.back, 0);
    gl.viewport(0, 0, this.statesize.x, this.statesize.y);
    gl.bindTexture(gl.TEXTURE_2D, this.textures.front);
        .attrib('quad', this.buffers.quad, 2)
        .uniform('state', 0, true)
        .uniform('scale', this.statesize)
        .draw(gl.TRIANGLE_STRIP, 4);
    return this;

First, bind the custom framebuffer as the current framebuffer with glBindFramebuffer(). This framebuffer was previously created with glCreateFramebuffer() and required no initial configuration. The configuration is entirely done here, where the back texture is attached to the current framebuffer. This replaces any texture that might currently be attached to this spot — like the front texture from the previous iteration. Finally, the size of the drawing area is locked to the size of the simulation state with glViewport().

Using Igloo again to keep the call concise, a fullscreen quad is rendered so that the fragment shader runs exactly once for each cell. That state uniform is the front texture, bound as GL_TEXTURE0.

With the drawing complete, the buffers are swapped. Since every pixel was drawn, there’s no need to ever use glClear().

The Game of Life Fragment Shader

The simulation rules are coded entirely in the fragment shader. After initialization, JavaScript’s only job is to make the appropriate glDrawArrays() call over and over. To run different cellular automata, all I would need to do is modify the fragment shader and generate an appropriate initial state for it.

uniform sampler2D state;
uniform vec2 scale;

int get(int x, int y) {
    return int(texture2D(state, (gl_FragCoord.xy + vec2(x, y)) / scale).r);

void main() {
    int sum = get(-1, -1) +
              get(-1,  0) +
              get(-1,  1) +
              get( 0, -1) +
              get( 0,  1) +
              get( 1, -1) +
              get( 1,  0) +
              get( 1,  1);
    if (sum == 3) {
        gl_FragColor = vec4(1.0, 1.0, 1.0, 1.0);
    } else if (sum == 2) {
        float current = float(get(0, 0));
        gl_FragColor = vec4(current, current, current, 1.0);
    } else {
        gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);

The get(int, int) function returns the value of the cell at (x, y), 0 or 1. For the sake of simplicity, the output of the fragment shader is solid white and black, but just sampling one channel (red) is good enough to know the state of the cell. I’ve learned that loops and arrays are are troublesome in GLSL, so I’ve manually unrolled the neighbor check. Cellular automata that have more complex state could make use of the other channels and perhaps even exploit alpha channel blending in some special way.

Otherwise, this is just a straightforward encoding of the rules.

Displaying the State

What good is the simulation if the user doesn’t see anything? So far all of the draw calls have been done on a custom framebuffer. Next I’ll render the simulation state to the default framebuffer.

GOL.prototype.draw = function() {
    var gl = this.gl;
    gl.bindFramebuffer(gl.FRAMEBUFFER, null);
    gl.viewport(0, 0, this.viewsize.x, this.viewsize.y);
    gl.bindTexture(gl.TEXTURE_2D, this.textures.front);
        .attrib('quad', this.buffers.quad, 2)
        .uniform('state', 0, true)
        .uniform('scale', this.viewsize)
        .draw(gl.TRIANGLE_STRIP, 4);
    return this;

First, bind the default framebuffer as the current buffer. There’s no actual handle for the default framebuffer, so using null sets it to the default. Next, set the viewport to the size of the display. Then use the “copy” program to copy the state to the default framebuffer where the user will see it. One pixel per cell is far too small, so it will be scaled as a consequence of this.viewsize being four times larger.

Here’s what the “copy” fragment shader looks like. It’s so simple because I’m storing the simulation state in black and white. If the state was in a different format than the display format, this shader would need to perform the translation.

uniform sampler2D state;
uniform vec2 scale;

void main() {
    gl_FragColor = texture2D(state, gl_FragCoord.xy / scale);

Since I’m scaling up by four — i.e. 16 pixels per cell — this fragment shader is run 16 times per simulation cell. Since I used GL_NEAREST on the texture there’s no funny business going on here. If I had used GL_LINEAR, it would look blurry.

You might notice I’m passing in a scale uniform and using gl_FragCoord. The gl_FragCoord variable is in window-relative coordinates, but when I sample a texture I need unit coordinates: values between 0 and 1. To get this, I divide gl_FragCoord by the size of the viewport. Alternatively I could pass the coordinates as a varying from the vertex shader, automatically interpolated between the quad vertices.

An important thing to notice is that the simulation state never leaves the GPU. It’s updated there and it’s drawn there. The CPU is operating the simulation like the strings on a marionette — from a thousand feet up in the air.

User Interaction

What good is a Game of Life simulation if you can’t poke at it? If all of the state is on the GPU, how can I modify it? This is where glTexSubImage2D() comes in. As its name implies, it’s used to set the values of some portion of a texture. I want to write a poke() method that uses this OpenGL function to set a single cell.

GOL.prototype.poke = function(x, y, value) {
    var gl = this.gl,
        v = value * 255;
    gl.bindTexture(gl.TEXTURE_2D, this.textures.front);
    gl.texSubImage2D(gl.TEXTURE_2D, 0, x, y, 1, 1,
                     gl.RGBA, gl.UNSIGNED_BYTE,
                     new Uint8Array([v, v, v, 255]));
    return this;

Bind the front texture, set the region at (x, y) of size 1x1 (a single pixel) to a very specific RGBA value. There’s nothing else to it. If you click on the simulation in my demo, it will call this poke method. This method could also be used to initialize the entire simulation with random values, though it wouldn’t be very efficient doing it one pixel at a time.

Getting the State

What if you wanted to read the simulation state into CPU memory, perhaps to store for reloading later? So far I can set the state and step the simulation, but there’s been no way to get at the data. Unfortunately I can’t directly access texture data. There’s nothing like the inverse of glTexSubImage2D(). Here are a few options:

I’m reusing the “step” framebuffer for this since it’s already intended for these textures to be its attachments.

GOL.prototype.get = function() {
    var gl = this.gl, w = this.statesize.x, h = this.statesize.y;
    gl.bindFramebuffer(gl.FRAMEBUFFER, this.framebuffers.step);
    gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0,
                            gl.TEXTURE_2D, this.textures.front, 0);
    var rgba = new Uint8Array(w * h * 4);
    gl.readPixels(0, 0, w, h, gl.RGBA, gl.UNSIGNED_BYTE, rgba);
    return rgba;

Voilà! This rgba array can be passed directly back to glTexSubImage2D() as a perfect snapshot of the simulation state.


This project turned out to be far simpler than I anticipated, so much so that I was able to get the simulation running within an evening’s effort. I learned a whole lot more about WebGL in the process, enough for me to revisit my WebGL liquid simulation. It uses a similar texture-drawing technique, which I really fumbled through that first time. I dramatically cleaned it up, making it fast enough to run smoothly on my mobile devices.

Also, this Game of Life implementation is blazing fast. If rendering is skipped, it can run a 2048x2048 Game of Life at over 18,000 iterations per second! However, this isn’t terribly useful because it hits its steady state well before that first second has passed.

Have a comment on this article? Start a discussion in my public inbox by sending an email to ~skeeto/public-inbox@lists.sr.ht [mailing list etiquette] , or see existing discussions.

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Chris Wellons

wellons@nullprogram.com (PGP)
~skeeto/public-inbox@lists.sr.ht (view)