Those strange things called FRACTALS

First of all, WHAT THE HELL IS A FRACTAL?

 A fractal is a never ending pattern that repeats itself at different scales. That's why some people call them self-similarity objets. Fractals are extremely complex. However, they are extremely simple to make.
They are made by repeating a simple process again and again. Actually, you have may seen many fractals, although you don't realise it.

Fractals can be find st anywhere. plants, animals, skies, oceans, galaxies, ect.

NATURAL FRACTALS: BRANCHES:

Fractals are found all over nature, spanning a huge range of scales. 

We find the same patterns again and again, from the tiny branching of our blood vessels and neurons to the branching of trees, lightning bolts, and river networks. 

NATURAL FRACTALS: SPIRALS:

The spiral is another extremely common fractal in nature, found over a huge range of scales.

Biological spirals are found in the plant and animaL kingdome, whereas, non-living spirals are found in the turbulent swirling of fluids and in the pattern of star formation in galaxies. 

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GEOMETRIC FRACTALS

Geometric fractals can be made by repeating a simple process. For instance, The Sierpinski Triangle is made by repeatedly removing the middle triangle from the prior generation. The number of colored triangles increases by a factor of 3 each step, 1,3,9,27,81,243,729, etc.

  The Koch Curve is made by repeatedly replacing each segment of a generator

shape with a smaller copy of the generator. At each step, or iteration, the total length 

of the curve gets longer, eventually approaching infinity. Much like a coastline, the 

length of the curve increases the more closely you measure it.

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ALGEBRAIC FRACTALS

We can also create fractals by repeatedly calculating a simple equation over and over. Because the equations must be calculated thousands or millions of times, we need computers to explore them.
The Mandelbrot Set was discovered in 1980, shortly after the invention of the personal computer.

1-  It starts by plugging a value for the variable ‘C’ into the simple equation below. Each complex number is actually a point in a 2-
dimensional plane. The equation gives an answer, ‘Znew’ .






2- Then we plug this back into the equation, as ‘Zold’ and calculate it again.


Generally, when you square a number, it gets bigger, and then if you square the answer, it gets bigger still. Eventually, it goes to infinity. This is the fate of most starting values of ‘C’. However, some values of ‘C’ do not get bigger, but instead get smaller, or alternate between a set of fixed values.
These are the points inside the Mandelbrot Set, all the values of ‘C’ cause the equation to go to infinity, and the colors are proportional to the speed at which they expand.

There are many and many types of algebraic fractals, depending on what kind of equation you choose.

To see more, click here