Solipsis @theinquisitivereceptacle - Tumblr Blog

reefbreland

A collection of decorative wax seals.

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中國 Tianjin Zhongshuge Library 2024 redesign: Li Xiang [X Living]

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Gallery of Fluid Motion, Imperial College London

[A. Kiyama, R. Rabbi, T. Truscott; 2021 Poster | Utah State University]

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Alexander Horned Sphere | James W. Alexander (1924)

A classic example of a pathological (counterintuitive) object in the mathematical field of Topology. It was discovered by James Waddell Alexander II upon realizing that his original 1924 proof of Schoenflies' Theorem in 3D was incorrect. He then crafted the Horned Sphere as a new topological proof for the wild embedding of a 2-Sphere in 3D.

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Newton Fractals of Complex Polynomial Functions ❁

𝒵𝓃+1 = 𝒵𝓃 – 𝑝(𝒵𝓃) / 𝑝'(𝒵𝓃)

𝑝(𝒵) -> Fig. 1–5: 𝒵³–1 | 𝒵⁴–1 | 𝒵⁵–1 | 𝒵⁶–1 | 𝒵¹⁰–1

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3D Projection of Mandelbrot Set's Real Axis Bifurcation Diagram 𖣂

𝓏ₙ₊₁ = 𝓏ₙ² + 𝑐 -> 2D Mandelbrot Set, complex sequence notation

𝑓𝑐(𝑥) = 𝑥² + 𝑐 -> Bifurcation Quadratic Map, real function notation

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Predictive Self-Assembly Polyhedra into Complex Structures [2012; P.F. Damasceno, M. Engel, S.C. Glotzer. Science, Vol. 337/6093] doi

Quasicrystals ∝

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The Mandelbrot Parameter Plane [M] + its infinite Julia Sets [Jc] ❆

It's often described by mathematicians as "the most complex object in all of existence," a "bottomless wonder," and "a dictionary for all quadratic functions." ~M