### Fractals

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Chapter 7 of "Texturing and Modelling - A Procedural Approach" By David Ebert et al

Fractals

**What is it?**

a geometrically complex object, with the complexity arising through ** repetition of form **over

*some range of scale(size)***Definition**

Imagine the object as a kind of cottage cheese, with lumps all of a particular size. Fractals can be built from it, by (1) scaling down the lateral size and height of the lumps (2) adding them back to the original lumps (3) do these several times - we have a FRACTAL!

Technically speaking,

Lateral Size : *frequency* of the function (*spatial frequency*)

Height : *amplitude*

Amount by which lateral size is changed : *lacunarity* (latin for *gap*) i.e imagine octaves in music

In computer graphics, all fractals must be Band-Limited - reason (1) violates Nyquist sampling limit and causes aliasing (2) infinite loop may occur.

**Good for?**

natural phenomena. eg, mountains repeating over a range, triangular fractals for snowflakes, fire, water

turbulence character : clouds, steam

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