What is iteration?

   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/