What is a fractal?

Question

What are fractals?

Is this is one of the concepts that is brought over from Mathematics to programming to simplify or solve a particular set of problems?

I am closing this question and have posted a related question

This is a real question, it just has nothing actually to do with programming (aside from the original poster's misguided belief that it is a programming technique) — TheTXI, Jan 14 '09 at 20:17
Well, there are 2 questions here. The first isn't a programming question and the answer to the second is a simple 'no.' — Tim Frey, Jan 14 '09 at 20:17
I should have worded my question better. I wanted to know if this is one of the concepts that was brought over from Mathematics to programming to simplify or solve a particular set of problems — Developer, Jan 14 '09 at 20:21
At this point since you have already generated so many unrelated answers, then I would say that you would better serve the community by removing this question and asking a clearer question. To be honest though, the wikipedia article answers your question. — EBGreen, Jan 14 '09 at 20:24
As I stated above, now we essentially have a completely new question that makes all of the presented answers useless. It would have been much better for this to stay closed and have the real question answered as a new question. — EBGreen, Jan 14 '09 at 20:51

score 3 · Answer 1 · edited May 23 '17 at 10:32

3

If you want to know about fractals in a general non-programming way, I would suggest looking at a general non-programming site. Wikipedia has a good article on them. If you want to know about programming fractals, I would suggest looking at this already asked question:

How to program a fractal

It even has a fractal tag.

edited May 23 '17 at 10:32

Community

1
1

answered Jan 14 '09 at 20:14

EBGreen

36,735
12
65
85

score 2 · Accepted Answer · answered Jan 14 '09 at 20:18

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.

A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

It is too irregular to be easily described in traditional Euclidean geometric language.

It is self-similar (at least approximately or stochastically).

It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

It has a simple and recursive definition.

http://en.wikipedia.org/wiki/Fractal

score 1 · Answer 3 · answered Jan 14 '09 at 20:12

its a type of self-similar shape, often grounded in a repeated mathematical function (but not necessarily). It has nothing to do with programming technique, but the easiest way to view one is to write a program to draw it. (drawing a fractal with pen-and-paper is pretty time-consuming)

By 'self-similar' i mean, if you keep zooming in on different parts of the fractal, it doesn't get any "smoother" or more linear, as would happen with a non-fractal shape. It's degree of complexity is invariant of the zoom level.

the Wikipedia page is pretty useful

score 1 · Answer 4 · answered Jan 14 '09 at 20:15

Look up Procedural Generation for one way of how fractals are used in programming. They are an excellent way of generating chaotic/seemingly complex data from a very simple source. The generated data often benefits from self-similarity and other bits of organzation that make the content make more sense to people.

What is a fractal?

4 Answers4