Mathe Vital BannerZentrum Mathematik BannerTUM Banner

Interactive material accompanying the book Indra's Pearls

(The applets on the following pages were all created using the mathematical software Cinderella.2».)

1. Geometric Transformations

Transfm.png
Translation
Rotation
Spiral Similarity
Reflections
Inversion

2. Complex Numbers

Add.png
Complex addition and multiplication (integral)
Complex addition and multiplication (generic)
Complex conjugation
Powers of a complex number

3. Complex transformations

Spiral.png
Complex transformations
Komplex transformation of a grid (advanced)
Geometric transformations as complex functions
Iterated geometric transformations

4. Möbius transformations

Moeb.png
Möbius transformations
Inverse of a Möbius transformation
Möbius transformations from the images of three points
Möbius transformations from two fixed points
Field lines
Möbius transformations and stereographic projection

5. Transformation groups

Kalei.png
Two translations
Dr. Stickler in the hall of mirrors
Angled mirrors
Kaleidoscopes
Wallpaper groups
Iterated similarity transformations

6. Iterated function systems

Plant.png
A little foretaste
An IFS plant
How an IFS is created
The role of probabilty
IFS from two similarities
Barnsley's fern
IFS from two Möbius transformations

7. Iterated Möbius Transformations

Shotky.png
Two circles
Schottky circles
Schottky circle dance
Limit sets

8. Examples from Indra's Pearls

Collier.png
The ribbon
The ribbon with twists
The necklace
Finishing touches for the necklace
Yet another degree of freedom
Grandma's recipe