A mathematical description of natural shapes in our nonlinear world

Details A mathematical description of natural shapes in our nonlinear world A mathematical description of natural shapes in our nonlinear world

2004-05-25

arxiv.org/abs/nlin/0405057v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

3 pages, 2 figures

Scientific paper

The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic representations of a vast diversity of natural shapes and patterns by incorporating diverse aspects of asymmetry and seeming disorder which are absent in the original Gielis' formula. It is also shown how diverse sequences resembling some natural-world pattern evolutions are also generated by such nonlinear formulas.

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