author : S. G. Hoggar

Contents:

1. Isometries
2. How isometries combine
   • the dihedral group
3. The braid patterns
4. Plane patterns & symmetries
5. The 17 plane patterns
6. More plane truth
   • Archimedean tilings • Coxeter graphs • Wythoff's construction
7. Matrix and vector algebra
8. Isometries in 3-space
9. Quaternions and rotations
   • complex numbers • quaternion in-betweening • Bezier curves
10. Fractals and nature
    • snowflakes • self-similarity • topological dimension • Cantor • Sierpinski
11. Basic topology
    • metric spaces • subspaces and product spaces • limits and closed sets • continuity • quotient spaces
12. Compact sets, connected sets, holes and homeomorphisms
13. The existence and uniqueness of fractals
    • Hausdorff distance • Fixed Point theorem • winding numbers
14. Iterated function systems
    • affine maps • factorising rotations into shears • finding an IFS • condensation • attractors
15. Addresses, measures, and the random iteration algorithm
    • Hausdorff dimension
16. Julia, Mandelbrot, and beyond
    • dynamics of iterated complex functions