Mandelbrot parapuzzle computed and visualized in Lean, advancing formal complex dynamics
geoffreyirving · x · 2026-10-28
Geoffrey Irving shared a figure computed in Lean (project cascade, commit 65e866f) visualizing the puzzle/parapuzzle correspondence for the Mandelbrot set at c₀=i:
- The dynamical plane of f(z)=z²+i has a dendrite K; rays at angles 1/7, 2/7, 4/7 land at the α fixed point, and the map Ξ(c)=hc⁻¹(c) carries the puzzle structure Pⁿ(c₀) onto the parapuzzle Yⁿ(c₀) in the parameter plane
- Near the Misurewicz tip, both planes are shown at matched scaling (Tan Lei factor A ≈ 0.800−0.400i); colored pixels agree at 93% between planes
- Angles use exact ray-tracing digits, potentials via escape, double precision in Lean; explicitly labeled "Display only, not certified"
A striking demonstration of AI-assisted formal mathematics (Lean) applied to frontier complex dynamics questions related to MHC.
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