lab.tsiongas.eu

Playgrounds that show their working.

Each project is one page: a live model to play with at the top and, underneath, a step-by-step explanation of why it behaves the way it does. Nothing on these pages is pre-drawn. The two previews below run on each project's own numbers.

One complex chain

zN(t) = ∑k=−NN ck eikt

N = 16

approximation error = –%

Mathematics · Fourier series

Fourier Epicycles

Chains of spinning circles redraw a dragonfly, a treble clef and Czechia from their Fourier series. Under the playground, 24 short steps build the idea up from high-school maths: waves and the unit circle, the averages that find each circle, complex numbers, and at the end writing any drawing down as one equation.

  • 6 shapes
  • up to 8192 circles per chain
  • 24 steps in 7 parts
Open fourier.lab.tsiongas.eu

From the feet: a lead writes upwards while the arrow points its way.

Physiology · Electrocardiography

Heart Vectors

A simplified 3-D heart in which an activation wave really spreads, voxel by voxel. Its sources add up to one heart vector, and each of the twelve leads reads that vector from its own side. Block a bundle branch and see why RBBB and LBBB look the way they do. The explainer goes from a single cell to both blocks in 16 steps.

  • 12 leads + 3-D view
  • normal, RBBB, LBBB, partial delays
  • 16 steps in 3 parts
Open ecg.lab.tsiongas.eu