Appendix · hands-on

Interactive Lab

THE FRACTAL LABORATORY

Six knobs. Most of the fair.

Instead of memorising eleven pictures, ask what happens when you turn one mathematical knob while holding the others still.

RuleWhat gets replaced? ScaleHow much smaller? IterationHow many repeats? RandomnessWhich itinerary? ProbabilityHow often each map? Initial conditionWhere do we begin?

QUESTION TO ASK

Change the replacement rule. What geometry survives?

Koch, Dragon and L-systems show that a tiny local rule can control a global shape.

TRY IT HERE

Koch chapter →Dragon lab →L-systems →

The experimental habit: change one thing, predict first, observe second, explain third.

Eleven fractals, each with its own page: adjust the parameters that define it, pick a colour scheme (or set your own two colours), and download the result as a PNG. Every change redraws instantly.