## what is a fractal?

Fractal art is a graphical representation of a mathematical formula.

The images are similar to nature's original art. We see these common shapes every day as clouds, snowflakes, feathers, and trees.

There is a consistent and repeated pattern to all things. Snowflakes and frost crystals are something most people are familiar with. When you look at them under a microscope, the more you zoom in the more you realize the pattern is similar and repeated. When creating a fractal image you manipulate triangles to change the look of the fractals. A computer program called a fractal generator is used. There are limitless combinations of form, color, and detail. This contemporary digital art form is unique and produces amazing and unconventional images. Thankfully the computer can do the billions of calculations needed to create these unusual and beautiful images.

## what is an algorithm?

An algorithm is a fancy sounding word for a set of instructions. But, it's just a way to solve a problem step-by-step.

Here is a sample algorithm to make a peanut butter and jelly sandwich:

Get a piece of bread

Spread peanut butter on one side

Get another piece of bread

Spread jelly on one side

Put the two pieces of bread with the peanut butter and jelly on them together

Eat it!

Not complicated but each step must be in the right order or you might end up with peanut butter on the outside of the bread.

To write an algorithm to create a fractal image you might tell the computer to:

Draw a triangle and label the three sides: 1 , 3, and 5

Select a point in the exact center of the triangle to be your current position

Move half the distance from your current position to the right side of the triangle.

Draw a 3mm circle here: this is your new current position

Repeat from step 3…

So you see, there is no end. The circle will continue to get closer and closer to the right side with the circles overlapping more and move. But they will never reach the rights side. Direction for the computer however, must be in a language the computer understands. That is math.

The algorithm for the image in the window is written on both the sides of the glass. It would take the computer about 24 hours to calculate all of these instructions. That's a lot of math! Thankfully, the computer writes the algorithm based on the numbers we assign to the 80 different patterns and 400 choices.