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New - Explore Julia sets - and their connection with the Mandelbrot set.
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The Filled-In Julia set with C = (0.25,0.55)
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This set has C = (-0.54, 0.6) which is in part of the Mandelbrot that has a
limit set period of 10.
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For C = (0, -1) the Julia set has no interior. It is thread-like.
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Here C = (-0.752, -0.04) which is not inside the Mandelbrot set.
The Julia set is a collection of disconnected points.
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C = (-0.752, -0.04) as in the previous example.
We have zoomed in on part of the set.
Inside the Mandelbrot Set
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Most pictures of the Mandelbrot Set show the set in black.
The interesting colours are in the area outside the set.
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First steps, inspired by an animation shared by jerekt.
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Orbit periods.
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Limit set periods.
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A Filled-In Julia set, associated with the Mandelbrot set..
Explore some mathematical ideas without doing the maths.
Interesting patterns can be made by choosing the colour for each point by some rule.
The simplest ones are based on distances.
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The distance from a point - circles
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Adding the distances from two points - ellipses
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Multiplying the distances, and weighting one of the points.
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This one might look similar, but it is calculated
using the rule that generates the Mandelbrot set.
What next?
Here are some other patterns. These are generated by more complicated rules.
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An iterated function system (IFS)
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Part of a Julia set
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Pattern produced by a turmite
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A limit set from mobius transformations
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A pattern based on two loxodromic spirals
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Part of Indra's necklace