Questions tagged [fractals]

For questions on fractals, which are irregular, rough, or "fractured" sets that often possess self-similar structure.

The term fractal, derived from the Latin fractus meaning "broken" or "fractured," was coined by Benoît Mandelbrot in 1975 in order to describe mathematical objects (shapes, sets, processes, etc.) which possess irregular or rough structure at all scales. While there is little consensus on the precise definition of the term, fractals are typically characterized by self-similarity. The Cantor set, Sierpinski carpet, Koch Snowflake, and Mandlebrot set are examples of fractal sets.

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What is a prisoner set + Escapee Set In Fractal Geometry

Are both prisoner sets and escapee sets only applicable in Mandelbrot sets, and does prisoner sets have to converge to zero or to any real number and do escapee sets have to converge to infinity? Thank you so much!
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Contractions which are conformal

Can someone give an example for a contraction which is also a conformal? I know that we call a contraction as conformal when it preserves angles. Even a hint would be helpful.
Grazel
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Normalise exponential numbers between 0 and 1

I'm creating a fractal visualisation. I want the colour per point to be based off the iteration final value, $f(z_{n})$, instead of the traditional: number of iterations before reaching a cut-off (usually when any component, real or imaginary, of…
Tobi
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Do you know what fractal this is?

I want to write a program and draw this fractal but I don't know the recursion step. Does anyone know any information about this fractal?
AdryL
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