Four simple rules, chosen at random, draw a perfect fern. No one programmed a leaf — the fern is the fixed point of the chaos, and every frond is a tiny copy of the whole.
Start at any point. Each step, roll a die: with probability 1% jump to the stem (rule 1); 85% shrink-and-slide to make the main body (rule 2); 7% each for the left and right fronds (rules 3 & 4). Every rule is a simple affine map — just multiply and add — yet the result is a fern with the exact geometry of real leaves. Fractals are nature's compression algorithm.