IA ideas library
Fractal and chaos IA ideas: self-similarity, dimension and sensitive dependence
Fractals and chaos look like advanced mathematics, but the core ideas sit on top of the syllabus: geometric series give the perimeter and area of a snowflake curve, logarithms give a fractal dimension, and a simple quadratic iterated over and over can behave unpredictably.
The danger is a beautiful but descriptive IA: pictures of the Mandelbrot set and a history of Benoit Mandelbrot earn few marks. Choose one object and ask a precise question about it that you can calculate, measure or prove.
Fractals & chaos ideas (8)
- Infinite perimeter, finite area: designing your own snowflake curveAA SLAI SLAA HLAccessible
- From steady to chaotic: the logistic map's period doublingAA HLAI HLAmbitious
- How fractal is a fern? Box-counting dimension from photographsAI SLAA SLAI HLAA HLSolid
- Why does a random game draw the Sierpiński triangle?AA SLAA HLAI SLSolid
- Inside or out? Proving the escape radius for Julia setsAA HLAmbitious
- Fold a strip, unfold it: the dragon curveAA SLAA HLSolid
- A sponge with no volume and infinite surface: the Menger spongeAA SLAI SLAA HLAccessible
- A fractal shortcut for the travelling salesman: ordering stops along a Hilbert curveAI HLAA HLAmbitious
Also relevant (5)
- Why does Pascal's triangle make a fractal?AA HLAA SLSolid
- Why is the main body of the Mandelbrot set a cardioid?AA HLAmbitious
- How long is a coastline? Measuring fractal dimensionAA SLAA HLAI SLAI HLSolid
- When does Newton–Raphson fail? Cycles, divergence and basins of attractionAA HLAA SLAmbitious
- Press cos again and again: when does fixed-point iteration converge?AA SLAA HLSolid
Frequently asked questions
Is a fractal IA suitable for SL?
Yes. Snowflake curves, Sierpiński shapes and box-counting dimension need only geometric series and logarithms. Keep the question precise and the calculations your own.
How do I avoid a fractal IA that is just pictures?
Ask a question with a numerical answer (what is the dimension, where does the period double, what is the limit of the area) and spend your pages calculating, testing and reflecting on that answer.
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