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The Worlds of Mandelbrot and Julia

The sequel to The Fractal Machine, for those who want to go further. A machine made of transistors computes with fractions — its own multiplier, addition, comparison — and draws by itself on three 128 × 128 screens: the Sierpinski triangle, the Barnsley fern and the Mandelbrot set. A switch turns Mandelbrot into Julia worlds: every position of the switches is a new world. 106,610 transistors.

The introduction and lessons 0–1 are free; the rest opens after purchase.

What is inside

  1. Introduction
  2. History: worlds nobody saw for a hundred years
  3. Lesson 1. The 128 × 128 screen: seven bits instead of six
  4. Lesson 2. Fractions: the point nobody sees
  5. Lesson 3. The multiplier: long multiplication, all at once
  6. Lesson 4. The Barnsley fern: a leaf from random jumps
  7. Lesson 5. The Mandelbrot set: z = z² + c
  8. Lesson 6. Julia worlds: a switch changes the universe
  9. Summary
  10. All the parts
  11. Instructions in pictures