Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature, Second Edition
Symmetry 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.
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affine linear map arithmetic rule average axes of symmetry bifurcation bifurcation diagram called cartesian coordinates chaotic dynamics Chapter choose color complex multiplication complex numbers construct cyclic symmetry decimal expansion define denote describe dihedral group dihedral symmetry discussion Dn symmetric equation example fixed point formula fundamental cell geometric hexagonal lattice holohedry ideas images initial point integers irrational numbers iterated function system large number linear map lines of symmetry mapping f mathematical mathematicians motion obtained odd logistic map parameter Pentagon pixel rule plane polygon polynomial mapping precisely predictions produce Pythagorean Pythagorean theorem real numbers reflectional symmetries repeating patterns result screen shadowgraph shown in Figure SierpiŽnski triangle square lattice square symmetry star strange attractors Suppose symmetric chaos symmetric fractals symmetric icons symmetric mappings symmetry creation symmetry group theorem tiling pattern torus turbulence vectors vertex wallpaper wallpaper groups wheelset whole number zero