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/

Thanks for giving such detailed description on iteration in sketches.It would be so much helpful for all the students who are seeking help to draw such kind of sketches during their engineering classes.

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