  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.
