Julia set shapes in the Mandelbrot set

[Duncan C]

Most people who are interested in fractals are familiar with how the shape of a Julia set echos the region of the Mandelbrot set it's taken from.

The reverse is also true. Hidden in the Mandelbrot set are little echos of Julia sets. The image below is not a Julia plot, but a standard Zn+1 = Zn + C mandelbrot set in the complex plain.

It's taken from a "baby Mandelbrot" on the real axis. I zoomed in to the "dragon" region of that baby mandelbrot, and then found a "grand-baby" Mandelbrot at the base of a dragon. I then zoomed in on a tendril just outside the "grand-baby" mandelbrot, and found the shape below, which looks VERY much like a Julia set.

 
 http://upload.pbase.com/image/77430718/original

The plot is centered on -1.6285474757381330, 0.0005260504563778, at a width of about 3.56E-10


Here's another example. This one looks like Fatou dust, but again, its actually a Mandelbrot plot.

 
 http://www.pbase.com/duncanc/image/75747128/original

This one was centered on -0.7702557119579104, 0.1130369146248582i. The width of the plot is about 2E-7.


Duncan C
 

[montitan]

On Wikipedia are some very nice photos of some Julia-Sets inside the Mandelbrot-Set, check here

i've made some very nice pictures of some of these sets myself, one of them is 560 MB big as it has a resolution of 16000 x 12000 






 

[lycium]

pray tell, if you have these magnificently sized images, why don't you post gloriously antialiased ones online?

all it takes is opening the highres image in some decent image editing app, resampling (not ignoring every Nth pixel!) to the final res, and posting that. you'll notice a night and day difference... surely as a mac user you're well aware of antialiasing issues, since you use such a bling bling os all the time?

[Duncan C]

On Wikipedia are some very nice photos of some Julia-Sets inside the Mandelbrot-Set, check here

Thanks for the link. I've looked, but my German is limited to one semester I took over 20 years ago, so I haven't been able to decypher the page..

i've made some very nice pictures of some of these sets myself, one of them is 560 MB big as it has a resolution of 16000 x 12000 

 

16000 x 12000?!? Wow, that's a big plot. Were you printing a plot at poster size? And how long did it take to render?


Duncan C

[Nahee_Enterprises]

On Wikipedia are some very nice photos of some Julia-Sets inside the Mandelbrot-Set, check here

Thanks for the link.  I've looked, but my German is limited to one semester I took
over 20 years ago, so I haven't been able to decypher the page..

When I tried the link, it said "Diese Seite existiert nicht", which in english means the site does not exist.  Then it proceeds to give options for searching or creating it.





 

[FractalMonster]

It's a fascinating phenomena probably observed by many fractal exploring people.
In my chaotic series,

http://klippan.seths.se/fractals/articles/

article "12) Julia-like barriers" is devoted to this phenomena

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Regards,
Ingvar