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An interactive dual-panel simulator exploring the one-parameter family of memory-coupled iteration maps E(n+1) = E(n)² + β·E(n−1), where β ranges continuously from −1 to +1. The top panel renders the escape-time fractal (Julia-like set) in real time for each β value. The bottom panel displays a rotatable 3D cone whose cross-sectional radius at each β represents the average radius of the corresponding connected set, visualizing the full parameter space as a geometric solid.
At β = +1 (emission, full memory), the map is E(n+1) = E(n)² + E(n−1) — the CCF Set, the nonlinear memory extension of C₂. The connected set contracts to its smallest radius. At β = −1 (absorption, inverse memory), the map is E(n+1) = E(n)² − E(n−1). At β = 0 (free space, no memory), the map reduces to E(n+1) = E(n)², the standard quadratic iteration, and the connected set is a near-circle at maximum radius.
The 3D cone encodes the conformal structure J(β)ᵀGJ(β) = βG from Proof 3, where β is the fifth coordinate e in the parent signature sig(3,2). The cone axis is the β parameter; each ring is the measured fractal boundary at that β. The resulting shape — wide at β = 0, contracting toward both endpoints — is the CCF light cone in parameter space.
Slider and preset buttons allow continuous β exploration. The fractal panel supports zoom (scroll/pinch), pan (drag), and adaptive iteration depth. The 3D cone supports mouse/touch rotation.
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Title CCF Light Cone
An interactive dual-panel simulator exploring the one-parameter family of memory-coupled iteration maps E(n+1) = E(n)² + β·E(n−1), where β ranges continuously from −1 to +1. The top panel renders the escape-time fractal (Julia-like set) in real time for each β value. The bottom panel displays a rotatable 3D cone whose cross-sectional radius at each β represents the average radius of the corresponding connected set, visualizing the full parameter space as a geometric solid.
At β = +1 (emission, full memory), the map is E(n+1) = E(n)² + E(n−1) — the CCF Set, the nonlinear memory extension of C₂. The connected set contracts to its smallest radius. At β = −1 (absorption, inverse memory), the map is E(n+1) = E(n)² − E(n−1). At β = 0 (free space, no memory), the map reduces to E(n+1) = E(n)², the standard quadratic iteration, and the connected set is a near-circle at maximum radius.
The 3D cone encodes the conformal structure J(β)ᵀGJ(β) = βG from Proof 3, where β is the fifth coordinate e in the parent signature sig(3,2). The cone axis is the β parameter; each ring is the measured fractal boundary at that β. The resulting shape — wide at β = 0, contracting toward both endpoints — is the CCF light cone in parameter space.
Slider and preset buttons allow continuous β exploration. The fractal panel supports zoom (scroll/pinch), pan (drag), and adaptive iteration depth. The 3D cone supports mouse/touch rotation.
Work type Script
Tags light-space, light-matter, captain cookie face, ccf simulator
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Identifier 2605135640435
Entry date May 13, 2026, 11:23 AM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 13, 2026.
Information available at https://www.safecreative.org/work/2605135640435-ccf-light-cone
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