标题： 我们非线性世界中自然形状的数学描述 显示英文标题

标题： A mathematical description of natural shapes in our nonlinear world

摘要： 这项工作展示了两个简单的数学公式的示例，这些公式是对Gielis公式的自然非线性修改（其中一个为推广）。这些公式涉及相当数量的参数，并通过结合对称性和看似无序的多种方面，提供了大量自然形状和图案的非柏拉图表示，而这些方面在原始的Gielis公式中是不存在的。还展示了如何通过这样的非线性公式生成类似于某些自然界模式演化的多样化序列。 显示英文摘要

摘要： 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.