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! |