Interactive Simulations

The solar system today, turning at a week a second, worked out as you watch. Open it →

Interactive Simulations

Accelerating the grasp of intensional, generative structure, with perception and relationality as carrier.

Start at the top and go down. First how big things are and what the ear and eye keep of them, then one point moving, then shapes, then many things moving at once, then maps of ideas. Or see every simulation grouped by subject.

Perception

scale, sound, color

  1. 01

    Where the Names Run Out

    Down sixty-five powers of ten, and how each picture was taken.

  2. 02

    The Pitch Circle

    A note is how fast a wave turns. Twice as fast is the same note, an octave up.

  3. 03

    Sampling and Aliasing

    A recording is the wave’s height, written down thousands of times a second.

  4. 04

    The Color Circle

    The eye keeps three numbers from a light; two of them place its color.

  5. 05

    What a Screen Can Show

    Three lights mix. A screen shows only what lies between them.

Motion

trigonometry, complex numbers, calculus, gravitation

  1. 06

    Six Names for One Point

    A point walks a circle. Sine, cosine and the rest are lengths hanging off it.

  2. 07

    Complex Multiplication

    Two arrows multiply: the turns add and the lengths multiply.

  3. 08

    Rate of Change

    Mark where the ball is, wait, mark it again; divide; shorten the wait.

  4. 09

    The Solar System

    Pick any date from 1000 BC to 3000 AD and see where the planets were.

Geometry

solids, polytopes, mirrors, symmetry

  1. 10

    Platonic Solids

    The five solids whose faces and corners are all alike.

  2. 11

    Regular Polytopes: The Dimensional Ladder of Perfection

    The same perfect shapes in four, five and six dimensions.

  3. 12

    The Hexagonal Cell: Symmetry Beyond the Frame

    Six mirrors unfold into a honeycomb, then lift into four dimensions.

  4. 13

    The Infinity Cell: Standing Inside a Reflection Group

    Standing inside a mirrored dodecahedron.

  5. 14

    Crystal Amplituhedron: Symmetry as Boundary

    Every crystal symmetry on the boundary of one cone.

  6. 15

    Periodic Table Topology

    The elements as a lattice, with the loops the flat table tears.

Particles

fluids, flocks

  1. 16

    Fluid Dynamics Simulation

    Thousands of particles, each pushing on its neighbors.

  2. 17

    Boids Flocking Simulation

    A flock from three rules.

Graphs

networks of terms and ideas

  1. 18

    Ordinary Language Understanding

    Sixty mathematical terms, each given plainly, linked by what they need.

  2. 19

    Grokking Constellation Network

    Thirty-two ideas across physics and mathematics, joined where one becomes another.

Every simulation, grouped by subject