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Fractal

Ontology

A mathematical set that has a non-integer and constant Hausdorff dimension; a geometric figure that is self-similar at all scales.

Axiology

A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales.

In describing partly random or chaotic phenomena such as:

  • Evolution
  • Crystal growth
  • Fluid turbulence
  • Galaxy formation

Fractal Deep Dives

Fractal deep dives display the depth & diversity of a fractal.

Fractal Zoom (youtube.com)

Mandelbrot Zoom (youtube.com)

Mandelbrot fractal deep zoom 21 2^1116 HD (youtube.com)

Burning Ship Fractal Deep Zoom Animation (youtube.com)

Mandelbrot zoom. 10^275 (2.1E275 or 2^915) (youtube.com)

Last Lights On - Mandelbrot fractal zoom to 6.066 e228 - vimeo.com

Cosmic Scale

The Cosmic Scale

Epistemology

Cultural Definition

fractal (wiktionary)

Noun

(mathematics) A mathematical set that has a non-integer and constant Hausdorff dimension; a geometric figure that is self-similar at all scales.

(figuratively) An object, system, or idea that exhibits a fractal-like property.

Fractal (Wikipedia)

Pattern Expression

Fractal is a pattern that is applicable anywhere in Existence.