A fractal art generator: a maths EPQ idea
A title to start from
How can iteration with complex numbers generate fractal art, and why is the Mandelbrot set's edge so intricate?
Why it works as an EPQ
The artefact is a program and a set of images; the mathematics of iteration explains what you see.
Scope and difficulty
Solid. Solid. One family of fractals, written and explained by you.
The maths
Builds on these A Level topics: Sequences and series · Algebra and functions · Numerical methods.
You would learn:
- Complex numbers
- Escape-time algorithms
- Self-similarity
One possible plan
- Explain iteration of z ↦ z² + c and the escape radius of 2.
- Write a generator and choose a colouring method.
- Explore Julia sets and their link to the Mandelbrot set.
- Evaluate the images against your design brief.
Pitfalls
- Using someone else's code.
- Images with no mathematical explanation.
Where to start reading
- Search for: Mandelbrot set escape radius 2 proof
- Search for: Julia set connected Mandelbrot
Making something? Read the artefact guide first: an artefact still needs a research-based written report.
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All artefact projects ideas · all 93 ideas
Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.