David wrote:**The probability of an OFF cell turning into ON cell ('Birth') is 8C3 / 2^8 = 7/32 = 0.21875**

**The probatility of an On cell staying its state ('Surviving') is (8C2 + 8C3) / 2^8 = 21/64 = 0.328125**

Those are first approximations only. Not all of the 256 cell environments occur with equal probability, for starters because the overall density of cells is not 0.5.

For some more accuracy, assume that the density of cells is ρ.

birth frequency B = 52ρ³(1-ρ)⁶

survival frequency S = 52ρ⁴(1-ρ)⁵ + 28ρ³(1-ρ)⁶

Then solve the equation B+S = ρ to get finer results.

Still life-like and oscillator-like behavior also complicate this. In some areas (e.g. isolated still lifes, or a large block of

zebra stripes) survival and abstinence may prevail until disturbed; in others (e.g. a large block of

venetian blinds), birth and death.

For better accuracy, considering larger areas and timescales could help, e.g. 4×4 → 2×2 transitions rather than 3×3 → 1×1; or 5×5 → 1×1 over 2 generations.

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Here's a hypothesis:

A. For all sufficiently large N, there are more N-cell pseudo still lifes than strict still lifes.

a1. FASLNTAM N-cell tieless pseudo still lifes than tieless strict still lifes.

a2. FASLNTAM N-cell tied pseudo still lifes than tied strict still lifes.

B. FASLNTAM N-cell tied still lifes than tieless still lifes.*

b1. FASLNTAM N-cell tied pseudo still lifes than tieless pseudo still lifes.

b2. FASLNTAM N-cell tied strict still lifes than tieless strict still lifes.

C. For any finite pattern of ON cells, either the shape cannot appear as a subset of any still life, or FASLN, there are more N-cell still lifes containing this pattern than not.

(Note that a1 & a2 implies A, and b1 & b2 implies B.)

Not much stats on the number of ties of N cells is available; I have no idea

*a priori* how the amounts of ties and pseudo still lifes should relate to each other for large N. The concepts seem just about on level with each other.

*Ties are the contiguous analogue of pseudo still lifes. A still life is tied if it can be divided into two or more

*contiguous* parts that are still lifes in their own right.