Zantema H. Playing with Infinity. Turtles, Patterns, and Pictures 2024

Textbook in PDF format

This is a book about infinity - specifically the infinity of numbers and sequences. Amazing properties arise, for instance, some kinds of infinity are argued to be greater than others. Along the way the author will demonstrate how infinity can be made to create beautiful ‘art’, guided by the development of underlying mathematics. This book will provide a fascinating read for anyone interested in number theory, infinity, math art, and/or generative art, and could be used a valuable supplement to any course on these topics.
What is this Book About?
Numbers of the Simplest Kind
More Complicated Numbers
Flavors of Infinity
Infinite Sequences
Turtle Figures
Programming
More Complicated Sequences
The Thue-Morse Sequence
More Finite Turtle Figures
Fractal Turtle Figures
Variations on Koch
Simple Morphic Sequences
Looking Back