TtTimes-Table Circle

Procedural · Scale 2

Times-Table Circle

Put 200 points evenly round a circle and join each one to the point k times further round. The multiplication table becomes a drawing, and the multiplier k decides which one.

What it is

Put 200 points evenly round a circle and number them 0 to 199. From each point i, draw a straight chord to point i × k, counting round the circle and wrapping past 199 back to 0. The multiplier k is the only number that changes.

Small multipliers give a curve with k − 1 lobes. At k = 2 it is the heart-like curve called a cardioid.

The plates

Five plates. The multiplier is 2, 3, 4, 7 and 51. Wherever a chord passes through the letters it is drawn heavier.

Safari stop · The times table, drawn · Multiplier (k)
  • x 2

  • x 3

  • x 4

  • x 7

  • x 51

Turn the dial on the safari →

The plates are drawn by mosaic, a small Python library of our own, built on numpy, scipy, shapely and contourpy. No image model is involved, and each plate is a flat-colour SVG under 45 KB. The word Ciao is the safari's constant: it sits in the same place on every plate.

What we did and found

The rule is one multiplication and one remainder per chord: the remainder of i × k after dividing by 200. Every plate uses the same 200 points, so the multiplier is the only difference between them.

What is open

The number of points is fixed at 200. We have not drawn the same multipliers on other numbers of points.

mosaic is not yet part of Platypus, our visuals engine. That is why this cell is marked as working and not as shipped: the page is our notebook on the element.

Composes with

Other cells in the table — most still to be walked into in coming sessions.