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Fields and Forms

@eigen.eng

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Physics meets Escher.

Inspired by a recent visit to an M.C. Escher exhibition, this animation uses a warped grid as a scaffold for an atlas of tessellated locally linear dynamical-system charts.

Each local cell carries its own phase portrait. The global nonlinear flow emerges by smoothly blending them together.

#Physics #digitalart #science #Geometry #mathart taken in London, United Kingdom by @eigen.eng

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4 months ago

The patterns we observe in nature often arise from underlying geometric structures.

These illustrations show the time evolution of an eighteen-dimensional physical system (the Fermi–Pasta–Ulam system) — a model used in physics to study how energy transfers between connected oscillators.

The first illustration presents a matrix of pairwise phase-space plots, showing how the system’s geometry changes as the nonlinearity varies across rows.

The subsequent illustrations zoom-in on the individual phase portraits, revealing the characteristic periodic trajectories that define the system’s high-dimensional geometry.

Through these geometric forms, we can see how fundamental physical laws give rise to structured, often intricate, patterns in motion.

#physics #geometry #hamiltonianmechanics #engineeringart taken in London, United Kingdom by @eigen.eng

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a year ago

The geometry of linear phase space governing a two-dimensional heat transfer system. taken in London, United Kingdom by @eigen.eng

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4 years ago

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