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      lex: "analysis.py enumerates every neighbour-independent substitution system in the two pre-registered families (225 + 2197 systems), iterates each from every single colour (7041 runs) until the string has at least 2^15 symbols, dies, becomes bounded or exceeds 40000 steps, and computes the subword complexity p(n) for n = 1..20 of the first <= 2^17 symbols of every growing run (5109 runs; 24 slow linear-growth runs are analysed at the ~20000 symbols they reached). The same statistics are computed for the pre-registered neighbour-dependent control family (1296 systems, 2592 runs, <= 2000 steps) and, exploratorily, for 1500 random three-context systems. The Thue-Morse and Fibonacci systems are compared with the OEIS b-files, and a random 2^15-bit string gives the complexity reference. Run time about 9 minutes (the slow linear-growth systems dominate)."
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      lex: "Measured: 231 maximum subword complexity p(20) over all 5109 growing neighbour-independent runs (random reference 32319) (n = 5109, exact). Interpretation: Wolfram\'s \'nested pattern\' is given a formal operational content as low (sub-exponential, at most polynomial) subword complexity, which is the standard combinatorial signature of self-similar/morphic sequences: the Thue-Morse, Fibonacci and Cantor examples he gives all have p(n) = O(n). Rules whose replacement for some colour is the empty string, or that keep every string bounded, are included in the enumeration but can only give finite or eventually periodic output, which is trivially nested; the complexity test is applied to growing runs only. The claim\'s second half (\'more complicated behaviour requires neighbour dependence\') is tested only in the direction that neighbour-dependent systems can exceed the complexity bound, as a check of discriminating power; the universal statement itself is tested by exhaustive enumeration of two finite families."
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