What Is the Definition of a Fractal?

San Quentin prisoner Steve Jones asks: What is a fractal?
In layman’s terms, a fractal is a pattern that repeats itself over and over again, but on different size scales.
Probably the most familiar example would be a snow-flake.

‘They are also used in modeling turbulence and blood vessel formation’

Think of it first as a 6-armed star, but then each of the “arms” ends in another 6-arme
Broccoli head
d star. Each arm of these little stars could also end in yet another six-arm star, ad infinitum.
Real snowflakes are not that perfect, but the one I have copied above starts to approximate the fractal pattern I am referencing.
I also found a cool picture of a broccolihead (on Wikipedia, I will admit) that displays the same concept.

The large structure comprises a number of smaller spikes, and each of these is made up of even smaller spikes.
Once again, a basic pattern is repeated on different size scales.
Among other uses, fractals are very important in computer modeling.
I have heard that they are used to build complexity into descriptions of natural phenomena, such as weather patterns.
Instead of modeling a boundary between two air masses as a simple line or plane, fractals can be used to generate an intricate interface that is likely to be much more realistic.
They are also used in modeling turbulence and blood vessel formation.
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