Self-similarity is the hallmark of hidden order beneath apparent chaos, a principle where patterns repeat across different scales through recursive rules. Far from mere coincidence, this phenomenon reveals how simple mechanisms generate complex structures—whether in fractal coastlines, branching trees, or spreading contagions. At its core, self-similarity arises from deterministic processes governed by feedback loops, recursion, and phase transitions, forming a universal language of form across nature and computation.

Rule 30, a one-dimensional cellular automaton devised by Stephen Wolfram, exemplifies how minimal rules produce intricate complexity. Starting from a simple binary configuration—often a single live cell—Rule 30 evolves through 30 deterministic steps,

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