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Program:  IFS Fractal Drawer
Author:  Michael White (mikewhite314@gmail.com)

Iterated Function Systems (IFS) is a way of generating fractals (shapes that often have self-similarity, meaning they look the same regardless of what scale you view them on).  

IFS uses matrices to map points to create fractals, an example being the program to create the Sierpinski Triangle Fractal found in the TI-83 Plus manual.  In this program, I have added four other fractals that are generated in the same way:  the Sierpinski Carpet Fractal, a cool-looking 5-sided crystal, what I call the x-fractal, and a fern (very neat).

At first, you will get a menu asking wether you want to generate a fractal now or recall the picture of one that you have already generated.  (Only choose to recall a picture if it has already been generated (duh!), and to generate or recall any fractal, its picture (if it has one) must not be archived.  Once you have chosen an option, you have to choose which fractal you want.

This archive contains:

Pic1.8xi - TI-83+ picture variable of the Sierpinski Triangle
Pic2.8xi - Sierpinski Carpet
Pic3.8xi - 5-sided crystal
Pic4.8xi - x-fractal
Pic5.8xi - fern

the gifs with self-explanatory names
this document
IFS.8xp

Credits:
I would like to thank Josh Nyer, who I made this program for when he was doing a project on fractals, for getting me interested in trying to make a program for him.
I got all the "IFS codes," which give the required information to create a program, from "Chaos and Fractals on the TI Graphing Calculator" by Linda Sundbye of the Metropolitan State College of Denver.  I couldn't have made the program without these tables, but the code is all by me (except for the Sierpinski Triangle, of course).
If you're looking for more, find this, because it also includes the Koch curve, some tree fractals, and the cantor maze, which I couldn't figure out.