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Author Topic: How distorted can a minibrot be?  (Read 2368 times)
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MateFizyChem
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« on: November 09, 2016, 10:02:46 PM »

Today I found this distorted minibrot. evil Can it get more distorted like this?


* dis.jpg (157.05 KB, 512x288 - viewed 142 times.)
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MateFizyChem
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« Reply #1 on: November 09, 2016, 10:04:03 PM »

Oops, I thought that I was in the Mandelbrot subforum.
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Sockratease
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« Reply #2 on: November 09, 2016, 11:18:40 PM »

Oops, I thought that I was in the Mandelbrot subforum.

 bubble gum

It is now!
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Chillheimer
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Just another fractal being floating by..


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« Reply #3 on: November 10, 2016, 09:54:47 AM »

AFAIK you only find distorted minibrots in the seahorse-valleys/spiral-valleys. the closer you get to the attach-point of the bulb, the more distorted the minibrot  will be. But distortion maxes out at a certain angle and the difference gets smaller and smaller if you go deeper into the valley.
Pretty sure someone here knows that angle and why that is - claude?
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DarkBeam
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« Reply #4 on: November 10, 2016, 12:00:44 PM »

I think there is no limit cheesy
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hobold
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« Reply #5 on: November 10, 2016, 02:17:20 PM »

I have been trying to find the "most distorted" minibrot before, but my search was unsystematic. Can anyone provide some guidance on how to find "very" distorted minibrots?

To measure and compare distortedness, I suggest looking at the relative position where the largest disk (i.e. the one with the main antenna) is attached to the minibrot's cardioid. The further away from the normal position (opposite to the cardioid's cusp) the main disk is, the more distorted I'd call the minibrot.

I have never seen a minibrot where the main disk was rotated more than sixty-something degrees away from its ordinary position. Has anybody ever found a minibrot with an asymmetry of 90 degrees or even more? (Edit: the example image by the thread starter would be rated thirtysomething degrees, I guess.)
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claude
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« Reply #6 on: November 10, 2016, 06:59:59 PM »

AFAIK you only find distorted minibrots in the seahorse-valleys/spiral-valleys. the closer you get to the attach-point of the bulb, the more distorted the minibrot  will be. But distortion maxes out at a certain angle and the difference gets smaller and smaller if you go deeper into the valley.

Yes I found that too.

Quote
Pretty sure someone here knows that angle and why that is - claude?

not me!  I did find some research from 1994, but it's just quantifying the distortions, not searching for the most distorted:

Warped midgets in the Mandelbrot set
A.G.Davis Philip, Michael Frame, Adam Robucci
Quote
Warped midgets in the Mandelbrot set have been measured, using an algorithm that allows the positions of the head, and cardioid atoms (north and south) of any midget to be found, once one has placed the cursor on the computer terminal somewhere inside any midget. We describe two distortions of midgets: linear distortions and angular distortions. When the north and south angles are plotted in the north/south angle plane, families of points are formed. The angle and distance measures of warped midgets from the Sea Horse Valley of the Mandelbrot set and from other sea horse valleys of midgets, whether on the Spike or on tendrils above atoms, all fall closely together in one part of the north/south plane. Measures of warped midgets from tendrils above the major atoms on the surface of the Cardioid fall closely together in another part of the north/south plane. This different way of looking at the Mandelbrot set offers an interesting way of studying the distortions of midgets.
http://www.sciencedirect.com/science/article/pii/009784939490099X
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MateFizyChem
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« Reply #7 on: November 10, 2016, 09:26:03 PM »

I found this cute apple. Small difference, big disappointement.  sad

Real number position: 0,25000102515011806826817597033225524583655
Imaginary number position: 0,0000000016387052819136931666219461
Zoom: 6,871947673*(10^10)

How about a competition for finding the biggest distortion(Wait, has the distortion even got a name?)?


* dejavu.jpg (149.88 KB, 512x288 - viewed 202 times.)
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xenodreambuie
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« Reply #8 on: November 10, 2016, 10:05:48 PM »

The largest minibrot in each elephant or similar shape in most valleys on the right side has similar distortion.

Looking at other formulas (without using any Abs modes or trig functions to really add distortion), it can get worse. Here are some in (z^5+z+1)/(2z^2-1)+c; the two smaller minis are mutants compared to the large one.


* Distorts.jpg (133.32 KB, 640x480 - viewed 244 times.)
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Regards, Garth
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MateFizyChem
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« Reply #9 on: November 10, 2016, 10:42:24 PM »

The largest minibrot in each elephant or similar shape in most valleys on the right side has similar distortion.

Looking at other formulas (without using any Abs modes or trig functions to really add distortion), it can get worse. Here are some in (z^5+z+1)/(2z^2-1)+c; the two smaller minis are mutants compared to the large one.
<Quoted Image Removed>
(I am hoping that I did not fail at quoting the image.)

Larvae! Kill them, before these parasites will eat us inside out!!!  canadian

But it seriously is as amazing to me, as the mandelbrot set is to a new person in fractals. happy
« Last Edit: November 10, 2016, 10:49:32 PM by MateFizyChem, Reason: grammar fix » Logged
claude
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« Reply #10 on: November 11, 2016, 07:49:05 PM »

some fun with conformal transformations cheesy

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MateFizyChem
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« Reply #11 on: November 11, 2016, 08:40:30 PM »

Well, I deduced that, the closer a minibrot to zero, the smaller is the difference between a neighbouring minibrot and the found minibrot when it comes to the distortion, so there probably is a limit to the distortion.(Have I made myself clear?)

I am suggesting to measure the distortion in degrees(or radians), because no half is smaller(I thought so  embarrass), the parts of the minibrot are simply rotated. The 2nd picture is distorted by around 35 degrees(WARNING: I DID NOT MEASURE IT EXACTLY; THE MEASUREMENT MIGHT BE WRONG).
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Sockratease
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« Reply #12 on: November 11, 2016, 10:37:22 PM »

some fun with conformal transformations cheesy

Reminds me of my new avatar image   afro

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MateFizyChem
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« Reply #13 on: November 12, 2016, 05:41:16 PM »

So, has anyone got a hypothesis or a theory?
Quote
How distorted can a minibrot be?
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claude
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« Reply #14 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:



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
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