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This paper studies the DNA code of eleven mammals from the perspective of fractional dynamics. The application of Fourier transform and power law trendlines leads to a categorical representation of species and chromosomes. The DNA information reveals long range memory characteristics.

Bifurcational instabilities of increasing complexity are described, with instructive and intriguing applications. Multiple folds in the gravitational collapse of a star triggers a discussion about possible sequencing of folds. Columns, rings and a quirky floating log illustrate safe and dangerous pitchforks, with self-weight models as lecture demonstrations. Localized buckling is employed by biologists using magnetic tweezers to twist a DNA molecule and evaluate a cutting and de-knotting enzyme. Unfolding of complex bifurcations into “structurally-stable” forms by a number (codimension) of perturbations illuminates the imperfection-sensitivity of shells, and the interactive buckling of a guyed mast at a hyperbolic-umbilic catastrophe. Spinning of primitive planets introduces secondary bifurcations, while Kirchhoff’s analogy is displayed for rods and spinning tops. Examples of gyroscopic stabilization and levitation mimic the “traps” that are used in modern experimental physics to hold in place individual electrons and neutrons.

This article is an informal auto-biographical memoir by Mike Thompson, reflecting in retirement on his scientific researches in nonlinear phenomena, wandering pictorially from shell buckling, through bifurcations and chaos to climate tipping points. Some ideas and advice to young researchers are offered whenever it seems appropriate. Two research groups at University College London, and their two IUTAM Symposia are given some prominence, as are the ten years editing the Philosophical Transactions of the Royal Society.