** Fractals**

**“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.

**Koch Snowflake **

- 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:

**The Bramandian Rectangle**

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.

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