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conway.md

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John Conway's Game of LiFO

This script implements John Conway's Game Of Life as the procedural kernel for multiple LFOs.

The game is played on a 128x32 field (the size of the OLED). Every pixel is a cell. On every step an empty space will spawn a new cell if it has exactly 3 neighbours. Cells with 2 or 3 neighbours stay alive. Cells with 1 or 0 neighbours die of loneliness. Cells with 4 or more neighbours die of overcrowding.

This program acts as a free-running LFO; it is not clockable externally.

On every step, a number of random new cells will also spawn, based on the CV input provided on ain. k2 acts as an attenuator for the signal on ain.

I/O Mapping

I/O Usage
din Clear the field & start a new random spawn
ain Offset control for spawn density
b1 Manual equivalent to din
b2 Manual equivalent to din
k1 Base spawn density
k2 Attenuverter for ain
cv1 - cv6 Output signals. See below for details

Outputs

The six outputs are stepped CV outputs, whose values vary according to the game state.

  • cv1: outputs 0-10V depending on the Shannon entropy of the entire field
  • cv2: outputs 0-10V depending on the ratio between the number of new births and the current population
  • cv3: outputs 0-10V depending on the ratio between the number of births and the number of deaths in the latest generation
  • cv4: outputs a 5V gate every generation
  • cv5: outputs a 5V gate signal if the number of births in the last generation was greater than the number of deaths
  • cv6: outputs a 5V trigger if the field has reached a point of stasis

Stasis Detection

Because of the modest computing power available, this program uses some simple statistics to infer if the game has reached a point of stasis. There is a chance that false-positives and false-negatives can be detected.

When the game is believed to have reached a state of stasis it will automatically reset, as if a signal had been detected on din. The field will clear and be filled with random data with a density governed by ain, k1, and k2.

The game is assumed to have reached a state of stasis under these conditions:

  1. At least 12 generations have passed since the last reset
  2. The number of game spaces that have changed from dead to alive or alive to dead is equal to zero OR
  3. The sum of population changes in groups of 2, 3, or 4 generations has a standard deviation of 1.0 or less and the absolute value of the mean of the group is less than 1.0.

To better-explain 3, consider the following 12 generations' of population changes:

[16, -17, 18, -14, 8, -23, 0, -3, 13, -12, 6, -5]

Grouping these changes into buckets of 2, 3, or 4 generations we produce these summed buckets:

Size 2: [-1, 4, -15, -3, 1, 1]
Size 3: [17, -29, 10, -11]
Size 4: [3, -18, 2]

We calculate the mean and standard deviation of each set of buckets, giving:

Size 2: -2.167, 6.69328
Size 3: -3.25, 18.08833
Size 4: -4.333, 9.672412

In this case none of the standard deviations nor means have a magnitude smaller than 1, so the system is not considered to be in stasis.

Conversely, given these population changes:

[-12, 6, 4, 2, -12, 6, 4, 2, -12, 6, 4, 2]

Size 2: [-6, 6, -6, 6, -6, 6] -> 0.0, 6.0
Size 3: [-2, -4, -6, 12]      -> 0.0, 7.071068
Size 4: [0, 0, 0]             -> 0.0, 0.0

we would assume we have reached stasis, as the mean and standard deviation of the size-3 buckets are less than 1.0.

LFO Rate Variablility

Because of the implementation of Conway's Game of Life, when the field is densely-populated, e.g. immediately after a reset with a high spawn rate, the outputs will change relatively slow. As cells die off and the field becomes more sparse the rate will increase. This is normal.

Patch Ideas

You can patch an external LFO into DIN to periodically reset the simulation before it reaches a state of stasis.

You can create interesting feedback by patching cv1-cv3 into ain and using the gate/trigger signals from cv4-cv6 to control the simulation reset rate & reset density.

If the variation in the LFO rate causes problems you can take the outputs from Conway and connect them to an externally-clocked Sample & Hold module. This will smooth out the changes in the update frequency of Conway.