“A fractal is a never ending pattern and a natural phenomenon. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems.”
If the replication is the same on every scale, it is called a self similar pattern.
An example of this the Menger Sponge:
- Begin with a cube
- Divide every face of the cube into 9 squares (imagine a Rubik’s Cube). This will sub-divide the cube into 27 smaller cubes.
- Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube. Thus leaving 20 smaller cubes.
- Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue infinitely.
- Begin with an equilateral triangle
- Replace the middle third (median) of every line segment with with a pair of lie segments that form an equilateral triangle.
- Erase the base of the triangle.
The Mandelbrot Set
On the complex plane, is the set of all points where:
How WE created this:
- Begin with a rectangle, labeling the length as X and the height as Y.
- Divide the large rectangle into four similar rectangles using the dimensions of 4/9X and 4/9Y. A cross-like shape should appear in the middle with the dimensions of 1/9X and 1/9Y.
- Repeat this process, dividing each triangle in the same manner an infinite amount of times.