A fern, a tree, a river delta, a lightning bolt — they look intricate beyond planning, yet each is built by repeating one tiny rule at smaller and smaller scales. Learn the rule and you can grow a whole forest from a single line.
Draw a stem. At its tip, draw two smaller stems. At each of their tips, two smaller again. That's recursion — a rule applied to its own output, over and over.
Add levels and a bare line becomes a tree. Every branch is just a tinier copy of the whole.
Take a straight line and replace its middle with a little bump. Now do the same to every segment you just made. And again.
You get a fractal — a shape that looks the same however far you zoom in. This one is the famous Koch snowflake.
Write the rule as letters: a symbol for "draw", symbols for "turn", and brackets for "remember this spot, branch, then come back." Replace every symbol with a small phrase, repeatedly, and read the result like turtle instructions.
That's an L-system — and a two-line grammar is enough to grow a convincing plant. Change its branching angle.
Real plants are never identical twins. Let each branch wobble its angle and length a little, and every plant grown from the same grammar comes out unique — yet unmistakably the same species.
Replant a few times and meet the family.
Everything in this chapter came from a rule rewriting itself. Now shape that rule with your hands: bend the angle, push the generations, tilt every branch toward the sun. Then press Mutate — six variants of your plant, each a single typo away, grow side by side. Click your favourite and mutate again. That loop — vary, select, repeat — is the engine of every garden on Earth.