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Fractals
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1. Iterated Function System
- Iterated function system 3 afine maps.
- Iterated function system 4 afine maps.
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2. Fractals using a slider
- The Sierpinski triangle from a slide in GeoGebra.
- Another example with a different array.
Fractals
José Manuel Dos Santos Dos Santos, Jul 18, 2018

In this book I will put some fractals that I created with GeoGebra. I will also compare the constructions I made a few decades ago with JavaSketchPad. I hope it can be useful to someone. References: Peitgen, H., Hartmut Jürgens, and Dietmar Saupe. "Fractals for the classroom: part one. Introduction to fractals and chaos. With a foreword by Benoit B. Mandelbrot." Springer Science & Business Media, 1992. Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. Fractals for the classroom: part two: complex systems and mandelbrot set. Springer Science & Business Media, 2012.
Table of Contents
- Iterated Function System
- Iterated function system 3 afine maps.
- Iterated function system 4 afine maps.
- Fractals using a slider
- The Sierpinski triangle from a slide in GeoGebra.
- Another example with a different array.
Iterated Function System
A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image compression techniques.
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1. Iterated function system 3 afine maps.
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2. Iterated function system 4 afine maps.
Iterated function system 3 afine maps.


The Sierpinski triangle



The Sierpinski triangle from a slide in GeoGebra.


