# Exercises for Chaos Under Control

## Chapter 2: Iterated Function Systems

Iterated Function Systems (IFS) are an elegant way for generating
fractal images. These problems address some background and applications
of IFS.

In The Gasket Shall be our Guide
we explore basic transformation properties of the Sierpinski gasket.

In Making Some Other Pictures we
use some simple variations of the gasket rules to produce other fractals.

In Deterministic Iterated Function Systems
we use the "deterministic algorithm" (at each step, apply all the transformations
to every point of the picture) to generate a variety of fractal images.

In Random Iterated Function Systems
we use the "random algorithm" (start with a point and apply the transformations
one at a time, in random order, each time to the point produced by the
previous application) to generate a variety of fractal images.

In Pictures from Nature we generalize the
transformations, allowing for squashing and skewing to produce pictures
more closely resembling natural objects.

In Collage Theorem Problems we consider
"inverse problems:" starting with a fractal picture, how would we find the
transformations to make that picture?

In Coloring we use transformations to assign
"addresses" to regions of the fractal, and employ these addresses to color the
picture.

In What is Random? we find what aspects of
"random" are needed in the random algorithm.

Return to Exercises Introduction

Go to Chapter 1 exercises

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Go to Chapter 4 exercises

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Go to Chapter 7 exercises

Go to Chapter 8 exercises

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