Recursion · Self-similar structures

Fractal Tree

Apply one branching rule recursively. Self-similar structures, made tangible.

A fractal tree is built by one rule: a branch grows two smaller branches at a fixed angle, each of which grows two smaller branches, forever. Stop after N iterations and you have a tree. Recursion — the function that calls itself — is the natural language for any self-similar structure.

Branch Depth: 6Branch Angle: 25°Branch Length: 55px

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What you just learned: This tree draws itself by repeating one simple rule: “draw a branch, then draw two smaller branches.” This is called recursion — a function that calls itself. Trees, rivers, and snowflakes all follow recursive patterns.

What’s happening under the hood

›Recursive function: `drawBranch(length, angle)`. Base case: length below threshold → stop. Recursive case: call `drawBranch(length × 0.7, angle ± 30°)` twice.
›Each recursion level doubles the branch count: depth 5 = 32 leaves, depth 10 = 1024, depth 20 = ~1 million. Exponential growth is exactly what recursion expresses.
›Recursion appears throughout CS: tree traversals, parsers, search algorithms, divide-and-conquer sorts (merge sort, quick sort), and the call stack itself.

Dig deeper

Phase 1 · Functions

The concept you just explored is taught with full depth in the formal DURA curriculum.