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Summary
About the author
Preface
Prologue
Prelude

Part I The butterfly fractal
0 Kiss precise
0£®1 Apollonian gaskets and integer wonderlands
Appendix£º An Apollonian sand painting-the world's largest artwork
References
1 The fractal family
1£®1 The Mandelbrot set
1£®2 The Feigenbaum set
1£®2£®1 Scaling and universality
1£®2£®2 Self-similarity
1£®3 Classic fractals
1£®3£®1 The Cantor set
1£®3£®2 The Sierpinski gasket
1£®3£®3 Integral Apollonian gaskets
1£®4 The Hofstadter set
1£®4£®1 Gaps in the butterfly
1£®4£®2 Hofstadter meets Mandelbrot
1£®4£®3 Concluding remarks£º A mathematical£¬ physical£¬ and poetic mag¦Ð
Appendix£º Harper's equation as an iterative mapping
References
2 Geometry£¬ number theory£¬ and the butterfly£º Friendly numbers and kissing circles
2£®1 Ford circles£¬ the Farey tree£¬ and the butterfly
2£®1£®1 Ford circles
2£®1£®2 Farey tree
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Part II Butterfly in the quantum world
Part III Topology and the butterfly
Part IV Catching the butterfly

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