The Tap That Loses Count
Open a tap slowly and the drips are even. Open it more and they pair up, then go to four, then eight, and the doublings arrive faster each time at a rate that is the same in every system that does this.
numerics
3 projects
- 69
sounddeep - 48
Bulbs Know Fractions
Every bulb on the Mandelbrot set repeats with a period equal to the denominator of where it is attached, and between any two bulbs sits their Farey mediant.
- 38
Every Boundary Is All Three
Newton's method on z³ − 1 has three basins. Pick any point on any boundary between them and all three are arbitrarily close.