Physics / Math
Distance-field fractals
Surfaces with no mesh: a distance estimator and sphere tracing draw the whole thing.
Available for Windows
Makarov Math Suite
160 interactive modules bring geometry, topology, fractals, calculus, algebra, probability and algorithms into view. Rotate a surface, change a construction or follow an algorithm one step at a time.
160 modules · Page 1 / 8
Physics / Math
Deep zoom and the limits of precision
Zoom until the arithmetic gives out, then buy 22 more mantissa bits and watch the wall move.
Physics / Math
Physarum networks
A slime-mould swarm grows an optimal transport network from local rules.
Math
Chaos game
A die and a jump toward a random corner build a fractal nobody drew - Sierpinski's triangle, the fern, the dragon, the Menger sponge - the same from any start; drag the corners, change the jump, count the boxes and measure its dimension.
Physics / Math / Earth
Predator–prey (Lotka–Volterra)
An agent ecosystem: grass, herds, hunters - and Lotka–Volterra cycles.
Math
Cellular automata
One rule, many cells: Wolfram's 256 elementary rules stacked into a sheet, Life's glider gun and R-pentomino with their worldlines beneath the plane, and the 3D stencil rules that stay alive.
Math
Sandpile
Four grains spill to the neighbours - and out of one rule come avalanches of every size, a critical state and a fractal nobody drew; the identity of the sandpile group is spilled in front of you.
Math
Random walks
A swarm leaving home on the lattice: the cloud grows like √n, the endpoints go Gaussian, and in three dimensions two thirds never come back.
Physics / Math
Neural descent
A neural network learns digits live, drawn as physics: the loss landscape in 3D, gradient descent as a ball rolling downhill, momentum as inertia and minibatch noise as temperature.
Physics / Math
Hopfield memory
Damage a stored memory with a brush, predict whether it comes back, and watch the network repair it one neuron at a time - each flip lowering the energy by 2|h| - or fall into another memory or a spurious mixture, named as such.
Math
Julia sets
The filled Julia set of z² + c as a living island: drag c across the Mandelbrot map, watch the island morph - and shatter into dust the moment the critical orbit escapes.
Math
Complex mapping
A grid morphing under z², z³, 1/z, e^z, sin z, a Möbius map and the Joukowski map: the right angles survive everywhere f′ ≠ 0, and the probe circle measures |f′|, arg f′ and the winding at the critical points.
Some modules belong to more than one Suite. Shared experiments have one description here.