Editing Mandelbrot set (section)

===Image gallery of a zoom sequence===
The boundary of the Mandelbrot set shows more intricate detail the closer one looks or [[magnification|magnifies]] the image. The following is an example of an image sequence zooming to a selected ''c'' value.

The magnification of the last image relative to the first one is about 10<sup>10</sup> to 1. Relating to an ordinary [[computer monitor]], it represents a section of a Mandelbrot set with a diameter of 4 million kilometers.
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<gallery mode="packed">
Mandel zoom 00 mandelbrot set.jpg|Start. Mandelbrot set with continuously colored environment.
Mandel zoom 01 head and shoulder.jpg|Gap between the "head" and the "body", also called the "seahorse valley"<ref name=":7">{{Cite book |last=Lisle |first=Jason |url=https://books.google.com/books?id=h-czEAAAQBAJ |title=Fractals: The Secret Code of Creation |date=2021-07-01 |publisher=New Leaf Publishing Group |isbn=978-1-61458-780-4 |pages=28 |language=en}}</ref>
Mandel zoom 02 seehorse valley.jpg|Double-spirals on the left, "seahorses" on the right
Mandel zoom 03 seehorse.jpg|"Seahorse" upside down
</gallery>

The seahorse "body" is composed by 25 "spokes" consisting of two groups of 12 "spokes"<ref>{{Cite book |last=Devaney |first=Robert L. |url=https://books.google.com/books?id=GUpaDwAAQBAJ |title=A First Course In Chaotic Dynamical Systems: Theory And Experiment |date=2018-05-04 |publisher=CRC Press |isbn=978-0-429-97203-4 |pages=259 |language=en}}</ref> each and one "spoke" connecting to the main cardioid. These two groups can be attributed by some metamorphosis to the two "fingers" of the "upper hand" of the Mandelbrot set; therefore, the number of "spokes" increases from one "seahorse" to the next by 2; the "hub" is a [[Misiurewicz point]]. Between the "upper part of the body" and the "tail", there is a distorted copy of the Mandelbrot set, called a "satellite".

<gallery mode="packed" heights="180">
File:Mandel zoom 04 seehorse tail.jpg|The central endpoint of the "seahorse tail" is also a [[Misiurewicz point]].
File:Mandel zoom 05 tail part.jpg|Part of the "tail" – there is only one path consisting of the thin structures that lead through the whole "tail". This zigzag path passes the "hubs" of the large objects with 25 "spokes" at the inner and outer border of the "tail"; thus the Mandelbrot set is a [[Simply connected space|simply connected]] set, which means there are no islands and no loop roads around a hole.
File:Mandel zoom 06 double hook.jpg|Satellite. The two "seahorse tails" (also called ''dendritic structures'')<ref>{{Cite book |last=Kappraff |first=Jay |url=https://books.google.com/books?id=vAfBrK678_kC |title=Beyond Measure: A Guided Tour Through Nature, Myth, and Number |date=2002 |publisher=World Scientific |isbn=978-981-02-4702-7 |pages=437 |language=en}}</ref> are the beginning of a series of concentric crowns with the satellite in the center.
File:Mandel zoom 07 satellite.jpg|Each of these crowns consists of similar "seahorse tails"; their number increases with powers of 2, a typical phenomenon in the environment of satellites. The unique path to the spiral center passes the satellite from the groove of the cardioid to the top of the "antenna" on the "head".
File:Mandel zoom 08 satellite antenna.jpg|"Antenna" of the satellite. There are several satellites of second order.
File:Mandel zoom 09 satellite head and shoulder.jpg|The "seahorse valley"<ref name=":7" /> of the satellite. All the structures from the start reappear.
File:Mandel zoom 10 satellite seehorse valley.jpg|Double-spirals and "seahorses" – unlike the second image from the start, they have appendices consisting of structures like "seahorse tails"; this demonstrates the typical linking of ''n'' + 1 different structures in the environment of satellites of the order ''n'', here for the simplest case ''n'' = 1.
File:Mandel zoom 11 satellite double spiral.jpg|Double-spirals with satellites of second order – analogously to the "seahorses", the double-spirals may be interpreted as a metamorphosis of the "antenna".
File:Mandel zoom 12 satellite spirally wheel with julia islands.jpg|In the outer part of the appendices, islands of structures may be recognized; they have a shape like [[Julia set]]s ''J<sub>c</sub>''; the largest of them may be found in the center of the "double-hook" on the right side.
File:Mandel zoom 13 satellite seehorse tail with julia island.jpg|Part of the "double-hook".
File:Mandel zoom 14 satellite julia island.jpg|Islands.
File:Mandel zoom 15 one island.jpg|A detail of one island.
File:Mandel zoom 16 spiral island.jpg|Detail of the spiral.
</gallery>
The islands in the third-to-last step seem to consist of infinitely many parts, as is the case for the corresponding Julia set <math>J_c</math>. They are connected by tiny structures, so that the whole represents a simply connected set. The tiny structures meet each other at a satellite in the center that is too small to be recognized at this magnification. The value of ''<math>c
</math>'' for the corresponding ''<math>J_c</math>'' is not the image center but, relative to the main body of the Mandelbrot set, has the same position as the center of this image relative to the satellite shown in the 6th step.