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An interactive fractal explorer comparing the Mandelbrot Set (zₙ₊₁ = zₙ² + c) with the CCF Set (Eₙ₊₁ = Eₙ² + Eₙ₋₁). Both use identical computation — same z², same escape-time coloring, same palette — with one difference: the CCF Set replaces the constant c with the previous value E(n-1), adding one step of memory. The Mandelbrot Set (no memory) produces bulbs. The CCF Set (one step of memory) produces rays. The toggle between them demonstrates that memory transforms isotropic expansion into directional beam geometry. The CCF Set is mathematically equivalent to the complex Hénon map (b=1, c=0) and physically motivated as a phenomenological model of χ² (SHG) nonlinearity with cavity feedback: E² = phase doubling, E(n-1) = round-trip memory. Built in vanilla JavaScript with Canvas 2D rendering, pixel-level iteration, scroll/pinch zoom, and drag panning. Part of the Captain Cookie Face Universe (CCFU) — the Light-Matter Recurrence.
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Title CCF Set — Light-Matter Recurrence
An interactive fractal explorer comparing the Mandelbrot Set (zₙ₊₁ = zₙ² + c) with the CCF Set (Eₙ₊₁ = Eₙ² + Eₙ₋₁). Both use identical computation — same z², same escape-time coloring, same palette — with one difference: the CCF Set replaces the constant c with the previous value E(n-1), adding one step of memory. The Mandelbrot Set (no memory) produces bulbs. The CCF Set (one step of memory) produces rays. The toggle between them demonstrates that memory transforms isotropic expansion into directional beam geometry. The CCF Set is mathematically equivalent to the complex Hénon map (b=1, c=0) and physically motivated as a phenomenological model of χ² (SHG) nonlinearity with cavity feedback: E² = phase doubling, E(n-1) = round-trip memory. Built in vanilla JavaScript with Canvas 2D rendering, pixel-level iteration, scroll/pinch zoom, and drag panning. Part of the Captain Cookie Face Universe (CCFU) — the Light-Matter Recurrence.
Work type Script
Tags eₙ₊₁ = eₙ² + eₙ₋₁, ccf set, light-matter recurrence, captain cookie face, ccf simulator
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Registry info in Safe Creative
Identifier 2604275411578
Entry date Apr 27, 2026, 8:29 AM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date Apr 27, 2026.
Information available at https://www.safecreative.org/work/2604275411578-ccf-set-light-matter-recurrence
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Registration: 2604275411578
