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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > How distorted can a minibrot be?
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Author Topic: How distorted can a minibrot be?  (Read 25185 times)
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MateFizyChem
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« Reply #15 on: November 12, 2016, 07:32:59 PM »
Quote from: claude on November 12, 2016, 06:38:59 PM
Here's some visual evidence showing the convergence to a limit of distortion in elephant valley, with the period doubling each frame:

<Quoted Image Removed>

locations:
Code:
      4 -1.565201668337550811e-01 + 1.032247108922831780e+00 i @ 1.697e-02
      8 4.048996651751222142e-01 + 1.458203637665893004e-01 i @ 2.743e-03
     16 2.925037532341934199e-01 + 1.492506899834379792e-02 i @ 3.484e-04
     32 2.602618199285006706e-01 + 1.667791320926506355e-03 i @ 4.113e-05
     64 2.524934589775105209e-01 + 1.971526796077277316e-04 i @ 4.920e-06
    128 2.506132008410751344e-01 + 2.396932642510365971e-05 i @ 5.997e-07
    256 2.501519680089798192e-01 + 2.954962325906881015e-06 i @ 7.398e-08
    512 2.500378219137852631e-01 + 3.668242052764790239e-07 i @ 9.185e-09
   1024 2.500094340031833728e-01 + 4.569478652064613658e-08 i @ 1.144e-09
   2048 2.500023558032561377e-01 + 5.701985912706845832e-09 i @ 1.428e-10
   4096 2.500005886128087162e-01 + 7.121326948562731412e-10 i @ 1.783e-11
   8192 2.500001471109009610e-01 + 8.897814201389539302e-11 i @ 2.228e-12


So I am assuming that the 1st hypothesis is (inaccurately measured) 30 degrees.
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hobold
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« Reply #16 on: November 13, 2016, 08:10:35 AM »
The distortion of such Minibrots is not inherited by the respective satellite minibrots. For example the main antenna is bent quite out of shape, but the satellite minibrot there is much closer to symmetrical than the parent.

I had no success trying to "shapestack" distorted minibrots on top of each other.
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Adam Majewski
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« Reply #17 on: November 13, 2016, 09:00:41 AM »
Do you know :
http://mrob.com/pub/muency/distortion.html
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greentexas
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« Reply #18 on: November 16, 2016, 03:10:31 AM »
Quote from: claude on November 12, 2016, 06:38:59 PM
Here's some visual evidence showing the convergence to a limit of distortion in elephant valley, with the period doubling each frame:

<Quoted Image Removed>

locations:
Code:
      4 -1.565201668337550811e-01 + 1.032247108922831780e+00 i @ 1.697e-02
      8 4.048996651751222142e-01 + 1.458203637665893004e-01 i @ 2.743e-03
     16 2.925037532341934199e-01 + 1.492506899834379792e-02 i @ 3.484e-04
     32 2.602618199285006706e-01 + 1.667791320926506355e-03 i @ 4.113e-05
     64 2.524934589775105209e-01 + 1.971526796077277316e-04 i @ 4.920e-06
    128 2.506132008410751344e-01 + 2.396932642510365971e-05 i @ 5.997e-07
    256 2.501519680089798192e-01 + 2.954962325906881015e-06 i @ 7.398e-08
    512 2.500378219137852631e-01 + 3.668242052764790239e-07 i @ 9.185e-09
   1024 2.500094340031833728e-01 + 4.569478652064613658e-08 i @ 1.144e-09
   2048 2.500023558032561377e-01 + 5.701985912706845832e-09 i @ 1.428e-10
   4096 2.500005886128087162e-01 + 7.121326948562731412e-10 i @ 1.783e-11
   8192 2.500001471109009610e-01 + 8.897814201389539302e-11 i @ 2.228e-12


The converging seems to be finite. For this reason, I'm guessing the fractal distortion has some sort of "limit". I remember thinking that if you were to zoom into a distorted Minibrot, it would have even more distorted Mandelbrots, and so forth, into complete non-Mandelbrot like shapes. The distorted Mandelbrots do not seem to have heavily distorted zoom-ups, but the parts are rearranged a bit.
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Chillheimer
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Just another fractal being floating by..


chilli.chillheimer chillheimer
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« Reply #19 on: November 16, 2016, 09:30:59 AM »
Quote from: greentexas on November 16, 2016, 03:10:31 AM
I remember thinking that if you were to zoom into a distorted Minibrot, it would have even more distorted Mandelbrots, and so forth, into complete non-Mandelbrot like shapes.
Nope, the distortion doesn't 'add up' to the next generation minibrot. The only distortion I ever encountered was in a valley. The deeper, the more distorted.
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greentexas
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« Reply #20 on: November 16, 2016, 01:31:08 PM »
You are correct; but that is what I used to think.
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Chillheimer
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« Reply #21 on: November 16, 2016, 03:47:55 PM »
sorry, misread that..
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--- Fractals - add some Chaos to your life and put the world in order. ---
greentexas
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Posts: 64
« Reply #22 on: November 16, 2016, 06:04:57 PM »
Don't worry; it's okay.
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vinecius
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Posts: 15
« Reply #23 on: October 08, 2017, 09:52:48 AM »
how is it that i get the same image near (0,0)? at a zoom level of 1 that is 1e0

* xx.png (206.78 KB, 600x800 - viewed 603 times.)
« Last Edit: October 08, 2017, 10:08:14 AM by vinecius » Logged
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