Continuous Life

Generalization of Conway's Game of Life to continuous floating-point state space, exhibiting fluid-like organic self-replicating solitons.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Decay Rate 0.05

Entropy dissipation rate

Mathematical Formulation

81 chars high

Analytical Equation

s^{t+\Delta t}(x,y) = \sigma\left( s^t(x,y), \iint K_{\text{outer}}(r) s^t(\mathbf{x}+\mathbf{r}) d\mathbf{r}, \iint K_{\text{inner}}(r) s^t(\mathbf{x}+\mathbf{r}) d\mathbf{r} \right)

Compact Formula

avg = (1/8) * Σ neighbors, s_{t+1} = (0.25 <= avg <= 0.45) ? s + 0.08 : s - 0.05

Renderer Logic

if (avg >= 0.25 && avg <= 0.45) {
  nextState[idx] = Math.min(1, current + 0.08);
} else {
  nextState[idx] = Math.max(0, current - 0.05);
}

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#cellular-automata #smoothlife #continuous #artificial-life #experimental #solitons

Author: Math Art Core Target: 60 FPS

Continuous Life

Live Parameters

Mathematical Formulation

Mathematical Tags

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