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6. Conway's Game of Life

View this tutorial on Google Docs external link Conway's Game of Life in StarLogo Nova

Description​

In this activity, you will be implementing John Conway's Game of Life (also called "Life") in StarLogo Nova. The setup for the Life game is an infinite grid where initially some cells are colored (holding the status "live"). Indicating which cells are alive in the beginning is the only action required of the player, as the game establishes its next stage based on the previous state of the grid.

Rules​

The way Life transitions from stage to stage is by updating each grid cell according to the following rules:

  1. Survival: A live cell with 2 or 3 live neighbors lives in the next stage (a neighbor is a cell that's horizontally, vertically or diagonally adjacent)
  2. Underpopulation: A live cell dies if it has fewer than 2 live neighbors
  3. Overpopulation: A live cell with more than 3 live neighbors dies
  4. Reproduction: A dead cell with exactly 3 live neighbors gets revived

Patches and Conway's Game of Life​

With the Patch features in StarLogo Nova version 3, we can implement Life! Patches represent the grids dividing the SpaceLand. SpaceLand is composed of 101x101 patches, and each patch has coordinates from -50 to 50 (inclusively), with the patch (0, 0) at the center. Because the SpaceLand has a finite number of grids, but Life works on an infinite grid, we will have live cells wrap around the SpaceLand (which will make cool patterns for spaceships).

Part 1: Setting Up Initial Patch Configuration​

Goals: Set a subset of Patches to be live

Helpful Coding Blocks​

BlockDrawerUse
Patch at x: y: blockEnvironmentGets the Patch at a specific coordinate. Can be used when working with traits.
set color blockTraitsChanges the trait of an agent, in this case changes the color.
reset terrain blockEnvironmentResets Patch traits: can choose between resetting color, height, custom traits, or everything.

Setup Code​

On the World page, program a few patches to be live once setup is pushed. One suggested configuration is a vertical column of 5 patches. For other interesting layouts, check the Initial Setup Suggestions at the end of this tutorial.

Setup code for initial patch configuration

Check your Progress!​

When you click setup, you'll see the vertical bar. If you turn on editing terrain mode, you can count and confirm its height is 5 patches.

Vertical bar of 5 patches

Part 2: Counting Live Neighboring Cells​

Goals: Learning to use variables when determining neighboring cells, and counting live cells

Steps​

  • Create variables for each neighboring patches
  • Set variables to correct coordinates, accounting for edge coordinates
  • Count the number of live neighbors

Helpful Coding Blocks​

BlockDrawerUse
var blockVariablesInitializes a variable to a given value.
set variable blockVariablesUpdates the variable to a new value. The variable is chosen from a dropdown, so in order to be updated, it needs to be initialized first.
value of blockVariablesGives the value of a given variable.
info

Variables only exist within the block of code they're declared in.

1. Count Live Cells​

To continuously count the number of live cells surrounding a certain cell, we can use the detection block counting the number of patches that are alive (color = black) within 1.5 steps, and assign it to a live_cells variable. Patches are only counted in this area if the center of the patch is within a radius of 1.5 (1.5 steps will count all the adjacent patches).

Count live cells code

2. Handle Edge Wrapping (X-axis)​

In order to make the grid "infinite", patches on the edges will wrap around and count live cells on the opposite edge as well. To do this, if a patch has an x of -50 or 50 (it is on the left or right edge), make it create a counting breed that sets its x to the opposite side and the very edge of the map (x=-50.5 or 50.5). Then increase live_cells by the amount of live patches counted by the counting breed within 1.4 steps (1.5 steps would unnecessarily count an extra patch).

Edge wrapping code for X axis

3. Handle Edge Wrapping (Y-axis)​

Then repeat the same steps but substituting x with y.

4. Handle Corner Wrapping​

If the patch is one of the 4 corner patches, make it add 1 to live_cells if the patch on the opposite corner diagonally is alive.

Corner wrapping code

Full Part 2 Code​

Here is the complete code for counting live neighboring cells, including all edge and corner wrapping logic:

Complete Part 2 code

Part 3: Apply Game of Life Rules and Set Custom Traits​

Now that we have the live cells count, we can proceed with applying the rules for the Patches.

1. Apply Game of Life Rules​

Because we essentially change the patches one by one, immediately changing the colors of the cell would interfere with counting live neighbors for other patches. Therefore we will have two custom traits that remember whether the patch will change its color.

In the Patch page, make two custom traits:

  • dies — will hold the value True if a patch is alive and will die in the next stage
  • lives — will be True when a dead patch becomes alive

If both dies and lives are False, it means the patch maintains its status in the next stage.

Custom traits setup

Death Rule​

A live patch will die if either: there's less than 2 live neighbors (underpopulation), or more than 3 live neighbors (overpopulation).

Death rule code

Birth Rule​

A dead patch will come to life if there's exactly 3 live neighbors (reproduction).

Birth rule code

2. Update All Patches​

Add a yield block to give enough time for all patches to update. Now, check the custom traits and update patch colors accordingly.

Update patches code

To reset the custom traits, set them to False at the beginning of the loop.

Reset traits code

Check your Progress!​

Toggle on the button run. If you've started with the vertical column, you will see the following progression. For other configurations, check that the program is running correctly by comparing it on conwaylife.com.

Phase 1

Phase 1

Phase 2

Phase 2

Phase 3

Phase 3

Phase 4

Phase 4

Phase 5

Phase 5

Phase 6

Phase 6

Phase 7

Phase 7

Phase 8

Phase 8

Initial Setup Suggestions​

The Game of Life has attracted a lot of interest over the years because of the multitude of interesting initial settings that make even more interesting layouts. There are a few types you might want to try in StarLogo Nova and see how it develops over time.

Still Lifes​

Forms that keep their structure throughout the game.

PatternRepresentationPatch Coordinates
BlockBlock(0, 0), (1, 0), (0, 1), (1, 1)
BeehiveBeehive(0, 1), (0, -1), (1, 0), (-1, 1), (-1, -1), (-2, 0)
CrossCross(1, 0), (-1, 0), (0, 1), (0, -1)

Oscillators​

Layouts that eventually repeat the same form, in a cycle.

PatternRepresentationPatch Coordinates
BlinkerBlinker(0, 1), (0, 0), (0, -1)
BeaconBeacon(-2, 2), (-1, 2), (-2, 1), (-1, 1), (0, 0), (1, 0), (0, -1), (1, -1)

Spaceships​

A pattern that returns to its initial form after a period, while gliding across the grid diagonally.

PatternRepresentationPatch Coordinates
GliderGlider(0, -1), (-1, 0), (1, -1), (1, 0), (1, 1)

Random Initial Setup​

Try initializing with random patterns and observe how the terrain changes over time.

Random setup code
Random setup result

Copyright 2024 MIT Scheller Teacher Education Program. Distributed under Creative Commons license CC BY-NC 4.0.