Would someone please describe what a fractal is?

Question

Would someone please describe what a fractal is?

Answer 1

A fractal is a function whose solution resolves into a fractional dimensional space. WHen you plot the solution, it is self-similar, meaning if you zoom in on the drawing, it looks the same as it does zoomed out.

"Problems with defining fractals include:



* There is no precise meaning of "too irregular".

* There is no single definition of "dimension".

* There are many ways that an object can be self-similar.

* Not every fractal is defined recursively.



"

Answer 2

A fractal is usually arrived at via a graph of the values of an iteration which do not escape off into infinity, and it is colored by the number of iterations for each starting point before they escape into "bigness", meaning they're definitely going to be infinite.



For example:



f(n) = f(n-1)^2 - 1

put in 1 for n.

f(1) = f(0)^2 - 1

f(0) = f(-1)^2 - 1

f(-1) = f(-2)^2 - 1



Eventually, you need to set a maximum number of iterations, and at that maximum, the last value of n is used instead of f(n). In this example, the f(1) does in fact spiral off towards infinity after just 3 iterations.

Answer 3

Fractals are beautiful fascinating designs of infinate structure & complexity, creating a sense of childlike wonder. The closest memory of a fractal may be from looking through a kaleidoscope as a kid. Enjoy them. :)