what are fractals??

Question

try the simplest answer you can....

Answer 1

A fractal, BY DEFINITION, is a set for which the Hausdorff-Besicovitch dimension strictly exceeds its topological dimension. (That little mathematical bit being said, here's the gist of it:)
In effect, they are usually fractional-dimensional (i.e., non-integral-dimensional) sets, however, a fractal may have an integral dimension (in that case, the fractal dimension may be 2 for instance, while the topological dimension is 1.)
A good example of a fractal is (the length of) any coastline.
Measure it with an atlas, and you will get a certain length.
Measure it with a mile-rule, and you will get a greater length, as you will now be including little inlets and peninsulas that were not visible in the atlas.
Measure it with a ruler, and you will get an even greater length, due to adding little mounds, rocks, puddles etc. that can now be measured around and which were ignored by the mile-rule.
Continuing in this manner, the length of the coastline will go to infinity as smaller and smaller measuring-sticks are used. The fractal dimension of the coastline is therefore greater than 1 (the dimension of a line), but less than 2 (the dimension of a plane), while its topological dimension remains 1. The actual value of the fractal dimension in this case depends upon the "jaggedness" of the coastline. For instance, the coastline of Finland is extremely "jagged", consisting of many fjords and peninsulas. In this case, the fractal dimension is higher (closer to 2) than for instance, the coastline of Australia, which is rather smooth comparatively.

NOTE TO "emptiedfull"
They are NOT functions for one, (fractals are sets) and the fuctions which DO describe fractals are certainly NOT necessarily irrational! Please do not answer questions if you do not have the expertise. You will only serve to confuse and misinform people.

NOTE TO NC
That is not quite right. If you look at a line, it still looks like the same line at 1000x. A line is not a fractal.

Answer 2

Take a cube: it has 3 dimensions.
Now take a plane, it has 2 dimensions.
Now, that a line: one dimension.

If you take your line, and make a bump in it, it is still one dimensional, but it invades a little in the second dimension.
(And you repeat the process: add several bumps on the bump; and several bumps on each of the small bumps, and so on, to infinity).

Now, how long is the line? Infinitely long, if each "bumping" process increased the length by a factor of 2, then the first bumping make the line twice as long, the second bumping twice again, so it is 4 times the length of the original, and so on.

So, you wonder, what is the dimension of a line that is infinitely long, and end up covering area, yet is not a plane? Well, it is somewhere between 1 and 2, with a value that has a fractional part. Hence, is is called "fractal".

(Same thing can be done with a plane with bumps in it, and ending having a dimention that is between 2 and 3)

Answer 3

OK, let's say you look at two pictures. One shows a certain object natural size; the other at 1000x magnification. If you can't tell which is which, congratulations, you are looking at a fractal.

Answer 4

They are graphic, colorful representations of algorhythms. Beautiful & psychedelic! UltraFractal is a program to create them, free 30 day trial.

Answer 5

they are irrational functional equations that tend to capture living patterns, especially order of magnitude details. part of string theory has dimensions that are like linear dimensions but are dissimilar to them in the way they directly connect the orders of magnitude. dimensions of space that shortcut through the orders of magnitude would be the key to most all of the undiscovered frontiers physics/science has to explore, yes?