# Fractals and Recursions

Discussion in 'Off-Topic' started by silver 2039, Oct 21, 2006.

1. ### silver 2039Deity

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What the hell are fractals and recursions? I can't figure out these definations. Damn wikipeida. I need to know in terms of math.

2. ### Erik MesoyCore Tester / Intern

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A fractal is an infinitely complex shape usually generated by means of (infinite) recursion. Recursion is the repetition of something (usually pattern-generating).

Take a look at the Koch Snowflake.

Recursion is, in this example, the process of putting a triangle on the middle third of each line, then putting a triangle on the middle third of each line, then putting a triangle on the middle third of each line, then...

A fractal is the result of this process.

Not all recursions lead to fractals and not all fractals are recursively generated, but most are.

3. ### silver 2039Deity

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So something like the Sierpinsiki's traingle?

4. ### Erik MesoyCore Tester / Intern

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An infinitely detailed Koch snowflake has a finite area (it's bounded inside a sphere) but an infinitely long border.

An infinitely detailed Sierpinski triangle has zero area, an outside border equal to the normal triangle, and infinite total border length.
(Math: The limit of (3/4)^n as n approaches infinity is zero.)

5. ### SyterionVoodoo Economist

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Recursion is when an instance of something causes another instance of it to be called, like a function in programming that calls itself. A fractal is a shape made by repeating shapes in a pattern, often recursively.

6. ### CruddyLeperUnworshipped Deity

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Fractal = shape with fractional dimensions.

You can think of something with 2 dimensions like a square. Or 3 dimensions like a cube.

Now try to imagine what happens when a shape has 2.3 dimensions.

"To iterate is human. To recurse is divine".

Imagine a simple program that takes a number, doubles it, and outputs the answer. Then it runs again with the result from the last cycle.

This cycling or "looping" is a crucial feature of recursion. Iteration is doing the same thing over and over - recursion is similar but can take it's data from the output of the last cycle.

Best book I have yet come across on the subject is "Fractals Everywhere" by Dr Michael Barnesley. Although that's more about iterated systems than recursion.

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