Observe the equisite sensitivity near the border: A point C just inside the Mandelbrot Set creates a connected Julia Set, while a point just outside the Set creates disconnected Julia Sets. As you zoom deeper into the edge of the Mandelbrot Set, watch the behavior of the Julia Set.
Wherever you zoom into the edge of the Mandelbrot Set, the Julia Set begins to take on the same appearance as the local area of the Mandelbrot Set.
As you go deeper, the Mandelbrot Set and the Julia Set from the corresponding location begin to resemble each other more and more closely. The only places where this is not true are the tiny replicas of the Mandelbrot Set which never appear in the Julia Sets.
Observe the relationship between the orbit diagram and the Julia Set. Wherever there's a black island-like Julia Set, the orbits are closed, that is, they stay finite. Wherever the Julia Sets are colorful - and disconnected - the orbits fly away to infinity. For the connected Julia Sets where C is inside the Mandelbrot Set , all the starting values of Z in the black, connected area will stay finite, whereas the starting values of Z from outside the black area will go to infinity. We call a black, connected Julia Set a "Basin of Attraction", because any value of Z inside the black area is attracted into a stable, finite orbit.
All other starting values of Z are repelled, and orbit away to infinity. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. What is the relationship between julia set and mandelbrot set? Ask Question. Asked 8 years, 11 months ago. Active 5 years, 5 months ago. Viewed 3k times. Improve this question. Micromega Micromega This has nothing to do with programming as far as I can see - I suggest it's moved to somewhere else in the SE network - mathematics?
Algorithm questions and directly related math are on topic Dale it's already been retagged :- — Philip Kendall.
PhilipKendall I see that now cheers : — Dale. For a julia, you iterate for z, with c being a constant. Show 5 more comments.
Active Oldest Votes. As I see you are new to Mandelbrot and Julia here are some definitions to see the relationship. Mandelbrot map: the map you calculate and visualize graphically Mandelbrot set: those points on the map that go to infinity which you usually paint black. Those shiny colored parts on the usually displayed Mandelbrot pictures are not part of the Mandelbrot set Continous map: where points on the set lies next to each other you can walk the whole map by starting from any point Island map: where points on the set lie isolated you cannot walk the whole map from a starting point There is only one Mandelbrot set and there are infinite Julia sets and some definition says the Mandelbrot set is the index set of all Julia sets.
Julia Sets. The Julia set is the boundary of the filled-in Julia set. For almost all c, these sets are fractals. The Mandelbrot set. Julia sets are either connected one piece or a dust of infinitely many points.
The Mandelbrot set is those c for which the Julia set is connected. Combinatorics of the Mandelbrot Set. Associated with each disc and cardioid of the Mandelbrot set is a cycle. There are simple rules relating the cycle of a feature to those of nearby features. From this we can build a map of the Mandelbrot set. Some features of the Mandelbrot set boundary. The boundary of the Mandelbrot set contains infinitely many copies of the Mandelbrot set.
In fact, as close as you look to any boundary point, you will find infinitely many little Mandelbrots. The boundary is so "fuzzy" that it is 2-dimensional. Also, the boundary is filled with points where a little bit of the Mandelbrot set looks like a little bit of the Julia set at that point.
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