Introduction

This kit is for those who want to go further: the sequel to the free Fractal Machine from the Hardware Basics series. In it, a circuit made of transistors computes with fractions and draws three famous fractals by itself on three 128 × 128 screens: the Sierpinski triangle, the Barnsley fern and the Mandelbrot set, which a switch turns into Julia sets.

Inside:

  • a 128 × 128 screen — seven-bit counters and a raster scan;
  • fractions — a fixed point, addition and subtraction;
  • a multiplier all at once — 14 × 14 bits, signed, in one clock;
  • the Barnsley fern — chance, a coefficient ROM and four multipliers;
  • the Mandelbrot set — z = z² + c for every dot, up to 32 repeats;
  • Julia sets — switch J and the 28 switches of the number c: every position is a world of its own.

How big it is

This is the biggest of our kits: the finished machine is 106,610 transistors and 9 resistors. The Fractal Machine had three thousand. Building it takes several evenings and needs care: the multiplier has 14 identical rows of 43 pins, lesson 6 has 59 reconnects. Repeating parts are easiest to paste ready-made — every lesson has a Cmd+I paste; build by hand once each thing the lesson explains — a multiplier row, a ROM column, the "escaped" check.

Every lesson has a ⚠ Common mistake box — these are mistakes that really happened while building this machine. None of them shows at once: the circuit works, but draws the wrong thing. So after every lesson — a check against the table.

What you need

The gates NOT, AND, OR, NOR, XOR and the DFF flip-flop from The Fractal Machine (lessons 0 and 1) — it is free. Everything else we build here.

What you get

Six lessons: the 128 × 128 screen → fractions → the multiplier → the Barnsley fern → the Mandelbrot set → Julia sets. At the end three screens draw side by side, each in its own way, and you can see it in the speed: the fern shows up in seconds, the triangle in a frame, Mandelbrot dot by dot, as on the home computers of the 1980s.