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Fractal Math, Chaos Theory & Research => Mandelbrot & Julia Set => Topic started by: miqel on December 04, 2010, 03:21:14 AM




Title: Pattern Variations on Mandelbrot 'needle' or tip
Post by: miqel on December 04, 2010, 03:21:14 AM
This is a project i did about 8 years ago, to illustrate the stunning variety of patterns to be found in even a somewhat featureless looking region like the tip above the largest minibrot on the needle.

I used a simple gradient from white to blue to black in a uniform way across all the images. Both to highlight the thin outlines of this region and also to give the series a standardized look similar to a series of microphotographs of ice crystals.

Here's a map of where the images all are nested, followed by thumbs
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/fract-000a.jpg)

Images from the needle tip (Sorry, the only format i have these in is long vertical image strips)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-6.jpg)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-7.jpg)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-8.jpg)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-9.jpg)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-10.jpg)
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbrot-set/mandelbrot-series-11.jpg)

I got sorta addicted to making these mandelbrots and the full series of images from the needle tip is about 140!  :)


Title: Re: Pattern Variations on Mandelbrot 'needle' or tip
Post by: jehovajah on January 25, 2011, 08:30:51 AM
The resemblance to ice crystal patterns and snow flakes is unquestionable.

At this scale it is probably  good approximation to molecular behaviour in cooled liquid mediums under a a simple environmental pressure-temperature variation. Very cool work miquel! ;D


Title: Re: Pattern Variations on Mandelbrot 'needle' or tip
Post by: tit_toinou on May 03, 2011, 08:11:40 PM
Awesome!
In fact, we can see theses kind of patterns everywhere on the Mandelbrot fractal... It was a good idea to only look onto the real axis :dink: .

I didn't understand how did you manage to be at the center of every "brotflake" ? Did you do it manually ?
Thanks!