Ikeda Map with Associated Voronoi Diagram
...and a lot of colours!
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Maths Meets Art

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Ikeda Map with Associated Voronoi Diagram
...and a lot of colours!
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Maths Meets Art
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Stills from a Sum of Neighbours cellular automaton on a grid of triangles. Animation only available at Patron.
Sprott's "Case F" strange attractor, demonstrating chaotic motion by following the trajectory of 100 Rainbow Dots. Here's the citation, on the off chance anybody wishes to look up the details: Sprott, J. C.: Some Simple Chaotic Flows. Phys. Rev. E, vol. 50, nr. 2, pp. R647-R650, 1994
This is the first 125 iterations of a "neighbour counting" cellular automaton. Each cell can be in one of two states, "on" or "off." The behaviour of each cell at iteration N+1 is defined by the number of neighbours in the 'on' state it has and whether the cell in question is on or off. An "on" cell with three or more "on" neighbours goes to "off", otherwise it stays "on." If a cell is "off" and has 1 or 2 neighbours switched "on", it swtiches "on." If it has three or more "on" neighbours, it stays "off." If it has zero neighbours "on", it remains "off."
Euler spirals.
100,000 colourful dots - but are they spiralling inward or outward?
Ikeda maps.
The Ikeda map is a 2-D iterative map with adjustable parameters and chaotic solutions for some parameter combinations. Here, 210 maps are plotted, each with an equal increase in a single parameter (usually called, "u"). As u is increased the colour plotted goes from deep red to white, via red and yellow shades. Try 7-day free trial of my Patreon to get early access to YouTube videos and see Patreon exclusive videos and images.
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Sum of Neighbours cellular automaton. Say "Hi," on YouTube if you watch!