Many of my Scratch projects are about fractals and
mathematical chaos. Examples are given below.

Both topics are products of the
computer age and are powered by a mathematical method known as

*iteration*. Iteration is sometimes confused with*looping*but it is a much deeper and more mathematically powerful tool than looping.
I have written a document that carefully,
step-by-step, compares the process of graphing y = f(x) with the iteration of y
= f(x). This information is basic for developing an understanding of the
mathematics that underlie fractals and chaos.

In the graphic shown below, the image on the left is the

*graph*of the function given in the center of the graphic with the parameter*c*varying from 0 to 8 in increments of one.
The image to the right is the

*iteration*of the same function with*c*starting at -0.5 and varying to -2.0 in 0.005 increments
For your free copy of this document send an email to
www.grandadscience@gmail.com.

**A Sample of My Fractal and Chaos Projects**

**Langton's Ant - Random Squares Experiment**

https://scratch.mit.edu/projects/41285348/

**Koch Snowflake**

https://scratch.mit.edu/projects/11128415/

**x^2+ c Plots**

https://scratch.mit.edu/projects/63919408/

**Chaos Game - Midpoint Formula**

https://scratch.mit.edu/projects/13649502/

**Mandelbrot Set [Featured Project - 4656 views]**

https://scratch.mit.edu/projects/10488782/