The Atlas [17 plates]

A cabinet of instruments.

Every plate is a small machine for seeing one idea move — drive the controls and watch the structure appear. Numbered as they were engraved; grouped by the field they belong to.

Number theory [2]

Plate I Prime Spiral A live field of primes in polar coordinates, built to make the hidden diagonal arms feel physical. Polar / Ulam / Sacks mappings Plate VI Ulam Spiral Integers wound onto a square spiral; the primes settle onto diagonal lines no one fully understands. Square spiral / residues

Complex analysis [1]

Plate II Riemann Zeta Phase, modulus, and the critical-line structure of the zeta function, tuned for intuition over textbook distance. Critical strip / partial sums

Discrete dynamics [1]

Plate III Collatz Conjecture The 3n+1 orbit as a branching instrument — deterministic steps tracing an unexpectedly organic tree. Orbit / tree growth

Chaos [2]

Plate IV Lorenz Attractor A strange attractor as a slow ribbon of instability, where tiny shifts in start become visible structure. 3D trajectory / sensitivity Plate XI Double Pendulum Two rods, one hinge, fully determined — yet copies a thousandth of a radian apart soon disagree completely. Hamiltonian / divergence

Learning [1]

Plate V MNIST Network Draw a digit and watch the signal move through a compact network, layer by layer, until it becomes a guess. Inference / live activations

Harmonic analysis [1]

Plate VII Fourier Series A chain of rotating circles summing into a square, sawtooth, or triangle wave — add harmonics and the corners sharpen. Epicycles / harmonics

Optimization [1]

Plate VIII Gradient Descent Follow the slope of a Rosenbrock valley to its floor; drop the ball anywhere and watch the classic zig-zag. Steepest descent / momentum

Probability [3]

Plate IX Central Limit Theorem Average n values from a lopsided source, repeat, and watch the means pile into a Gaussian — whatever the source. Sampling / convergence Plate XIII Bayesian Updating A flat prior over a coin’s bias, sharpened flip by flip into a posterior that concentrates on the truth. Beta–Bernoulli / inference Plate XV Markov Chain A memoryless walk over a few states whose long-run visit share converges to the stationary distribution. Transition matrix / stationarity

Fractals [1]

Plate X The Mandelbrot Set The boundary of bounded orbits of z ↦ z² + c, rendered as an ink mezzotint you can zoom into. Escape-time / zoom

Computation [1]

Plate XII Cellular Automata One local rule over a row of cells; 256 possible worlds, from Sierpiński order to genuine chaos. Elementary rules 0–255

Growth & number [1]

Plate XIV Phyllotaxis Seeds placed at the golden angle pack with no gaps and no overlaps; any rational angle makes spokes instead. Golden angle / parastichies

Linear algebra [1]

Plate XVI Eigenvectors A transform bends the grid and turns the unit circle into an ellipse; an eigenvector is a direction it only scales. Spectra / invariant directions

Language & meaning [1]

Plate XVII Bhagavad Gita offsite Seven hundred verses arranged in semantic space, exposing thematic neighborhoods and philosophical adjacency. Embeddings / 3D semantic map