reachtim

Art

Math art

Every one of these is a picture of an equation, a dynamical system, or some physical process behaving the way it does. I find it hard to look away from the fact that arithmetic produces things this pretty without being asked to.

Logarithmic-spiral surface rendered as a ribbed shell form.

Seashell Surface

A logarithmic-spiral surface that mirrors how mollusks deposit shell material as they grow.

Dense looping curve traced by a decaying pendulum drawing machine.

Harmonograph

The trace of a pendulum-driven drawing machine — decaying oscillations turned into curves.

Curved envelope formed by straight chords strung across a boundary.

String Art

Curves built entirely from straight lines strung between points around a boundary.

Klein bottle surface immersed in three dimensions, self-intersecting.

Klein Bottle

A non-orientable surface with no distinct inside or outside, immersed in three dimensions.

Biomorph-like form grown from an iterated function system.

Pickover

Biomorph-like forms grown from iterated functions, in the tradition of Clifford Pickover.

The two-lobed butterfly trajectory of the Lorenz system.

Lorenz Attractor

Trajectories of a chaotic system that never repeat, tracing the iconic butterfly shape.

Symmetric nodal pattern of a plate vibrating at resonance.

Chladni Plate

The standing-wave nodal pattern left by sound vibrating a plate at resonance.

Mottled Turing pattern of interleaved spots and stripes.

Reaction–Diffusion

Turing-style patterns that emerge from two chemicals diffusing and reacting at different rates.

Layered filament structure of the Clifford strange attractor.

Clifford Attractor

A strange attractor built by iterating a pair of trigonometric maps millions of times.

Three interwoven gravitational orbital paths.

Three-Body

Orbital paths from the classic gravitational three-body problem — chaotic and never periodic.

Twisted pseudosphere of constant negative curvature.

Dini Surface

A twisted pseudosphere of constant negative curvature, one of the classic surfaces of hyperbolic geometry.

Streamlines of particles traced through a vector field.

Flow Field

Particle paths traced through a vector field, visualizing the shape of an invisible flow.