How far can mu and sigma move before the glider dies or starts to multiply? The seed turns into a glider about 15 cells across: a yellow-green core (val near 1) inside a faint, partly open blue ring. It moves in a straight line at about 0.49 cells per tick, leaving one edge and coming back in on the opposite one.
Try this Raise sigma from 0.016 to 0.02 while the glider is running (it takes effect on the next tick). In most runs the glider splits within about 200 ticks and the pieces keep dividing until small rings cover the board, with mass rising from about 43 to about 520.
About this model Where it ends up
Lenia, published by Bert Wang-Chak Chan in Complex Systems (2019), is a continuous version of Conway's Game of Life: cell states are real numbers from 0 to 1, each cell's neighborhood is weighted by a smooth ring-shaped kernel, and a smooth growth function replaces the birth and survival rules. Some patterns keep their shape and move; the best known is the glider Chan named Orbium. This version uses Chan's kernel and growth function with a kernel radius of 10 cells on a 51 × 51 torus, and the default seed turns into an Orbium that keeps moving.
Each tick, every cell computes a potential u, the average of val over the cells less than 10 cells away, weighted by Chan's kernel shell exp(4 − 1/(r(1 − r))) with r = distance / 10. The weight is 0 at the center, largest halfway out and 0 at the rim. Then all cells update at once. val becomes clamp(val + dt × G(u), 0, 1), with growth G(u) = 2 exp(−(u − mu)² / (2 sigma²)) − 1, which is +1 when u equals mu and tends to −1 away from it. The sum runs in two passes (row sums, then columns), which gives the same u as the direct 2-D sum. mu, sigma and dt are read every tick; seed-pattern applies at Reset.
Differences from Chan's Orbium: he used R = 13, mu = 0.15 and sigma = 0.015, with the same dt of 0.1. R is 10 here to keep ticks fast. The seed is a fitted formula (an elliptical bump with a faint arc behind it, pointed in a random direction each run), not his recorded cells, but it settles into the same glider his cells settle into at these settings. At his mu and sigma it forms a glider in only about half of runs, hence the defaults of 0.145 and 0.016. Chan also describes multi-ring kernels and other shell and growth shapes; this version has only the single-ring exponential shell and Gaussian growth.
