Tiny example
Repeat a rule
Start with 2. Multiply by 2 and add 1 each time.
2 -> 5 -> 11 -> 23 -> 47. The rule is simple, but the behaviour grows quickly.
Iteration
Repeating a rule and watching what happens next.
Iteration means taking an output and feeding it back into the same rule. It is the engine behind many patterns, simulations and fractals.
Why it matters
Once a rule is repeated, small choices can become large patterns. This is why iteration belongs to fractals, sequences, simulations and feedback systems.
Things to watch for
- Changing the rule halfway through without noticing.
- Looking only at the final value instead of the path taken.
- Assuming a repeated rule must always settle into a simple pattern.
Where it connects
sequencesfunctionsiteration
Try it in a tool
RepetitionTransformationPattern
Mandelbrot and Julia Set Explorer
Zoom into fractal boundaries created by repeated complex iteration.
ExplorationRepetitionChangePattern
Logistic Map and Chaos Explorer
Iterate a simple recurrence and explore fixed points, cycles and chaos.
ExplorationRepetitionPatternChance
Cellular Automata Explorer
Explore how simple local rules create order, randomness and emergent patterns.
Exploration