Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature, Second EditionSymmetry suggests order and regularity whilst chaos suggests disorder and randomness. Symmetry in Chaos is an exploration of how combining the seemingly contradictory symmetry and chaos can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described. This second edition has been updated to include the Faraday experiment, a classical experiment from fluid dynamics which illustrates that increasing the vibration amplitude of a container of liquid causes the liquid to form surface waves, instead of moving as a solid body. This second edition also includes updated methods for numerically determining the symmetry of higher dimensional analogues of the images. As well as this, it contains new and improved quality images. |
Contents
OT111_ch2 | 35 |
OT111_ch3 | 54 |
OT111_ch4 | 89 |
OT111_ch5 | 102 |
OT111_ch6 | 129 |
OT111_ch7 | 139 |
OT111_appa | 171 |
OT111_appb | 177 |
OT111_appc | 183 |
OT111_bm | 195 |
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Common terms and phrases
actually appear arithmetic attractor average begin called chaos chaotic Chapter choose chosen color complex numbers complicated construct container contraction coordinates create cyclic symmetry define denote dependence describe discussion dynamics equal equation example experiment Figure fixed follows formula fractal geometric give given hexagonal hexagonal lattice holohedry ideas images integers iteration lattice lead linear logistic map look mathematical motion move multiplication natural Observe obtained origin parameter particular patterns pixel plane polynomial population positive possible precisely predictions present probability produce quilts rabbits random real numbers reflection regular repeating result rotation rule screen sequence shown side Sierpi´nski triangle simple square square lattice star structure Suppose symmetric icons symmetry term tiling translate turn vectors write