This fractal (sometimes called the Koch curve) is created by taking each line seqment, dividing it into three equal parts, then inserting an equilateral triangle into the middle section (and repeating this recursively). It is one of the earliest fractal shapes to have been explored. It is named after Swedish mathematician Helge von Koch.
This fractal is created by finding the midpoint of each side of the triangle, then creating a new triangle with these midpoints as the verticies. Repeat this process with each of the newly created triangles (except the one on the center). This pattern has appeared for centuries, but is named after Polish mathematician Waclaw Sierpinski
You may've noticed this fractal takes a little longer to load. That's because each pixel must pass through around 100 iteration of a calculation! The computer is checking whether the x value or y value of each coordinate, after performing some complex number operations, is greater than a specificed number. Each pixel is colored based on how many iterations it takes to get that point above the specified value.