ToolPrototype
Mandelbrot and Julia Set Explorer
Explore complex iteration, escape time, fractal boundaries and zooming into infinite detail.
Beauty in maths topic
Fractals and Infinite Detail
Fractals explore infinite detail from simple rules: repeated processes, self-similarity, roughness and patterns that look structured at many scales.
6
live pages
1
prototype tools
4
planned ideas
What this area includes
Mandelbrot and Julia sets from complex iteration
Fractal dimension and measuring roughness
L-systems, recursive growth and plant-like structures
Chaos games and iterated function systems
Newton fractals, roots and basins of attraction
Links between recursion, geometry, chaos and computation
Questions to explore
How can a tiny repeated rule create endless detail?
What does dimension mean when a shape is too rough to be a line but too thin to be an area?
Where do we see self-similarity in nature, art and computation?
When does iteration settle down, and when does it become unpredictable?
Working pages and tools
These are the pages currently available to open from this topic.
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
Fractal Dimension Explorer
Planned tool for measuring roughness, box-counting dimension and why dimension does not have to be whole.
ideaPlanned
L-Systems and Recursive Growth
Planned explorer for plant-like patterns generated by rewriting rules and recursion.
ideaPlanned
Chaos Game and IFS
Planned tool for generating fractals from repeated random or affine transformations.
ideaPlanned
Newton Fractals
Planned bridge between numerical methods, complex roots and basins of attraction.
Connected topics
themeLive
Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
themeLive
Emergence and Chaos
Simple rules producing behaviour that feels rich, alive or unpredictable.
themeLive
Geometry and Transformations
Matrices, complex numbers, transformations, symmetry and visual structure.
themeLive
Calculus and Change
Functions, rates, areas, differential equations and continuous change.
themeLive
Number and Structure
Irrational numbers, ratios, exactness, approximation and hidden structure.
themeLive
Topology and Surfaces
Shape, connectedness, holes, surfaces, knots and geometry that survives stretching.
How to use this section
The aim here is to make students zoom, predict and notice: change the rule, watch the pattern grow, then ask why the structure survives.