Title: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Chillheimer on October 11, 2014, 12:44:11 AM During the last years and countless zooms with Kalles Fraktaler I slowly started to get a grip of the inner workings of the M-Set.
I don't know if most of you are already aware of this, and to most people on our (fractal;)) planet this knowledge probably is useless.. But I would have loved to have some kind of guide or map to the M-Set when I started discovering it. There is the page by miquel, which I highly recommend to newbies: http://www.miqel.com/fractals_math_patterns/mandelbrot_fractal_guide.html But I was searching for some info about different yet similar zoom paths and how a small decision in the beginning does affect the later outcome. so here we go: 1, left side shows the main bulb 2 right side shows the same area but on the 2nd circle. this lengthens the end of every(!) branch by 1 extrabranch, with 2 sub-branches on each side. hard to explain, just take a close look: dl this for higher resolution: http://www.chillheimer.de/Fraktal/content/Parallel_combo.jpg (http://www.chillheimer.de/Fraktal/content/Parallel_combo.jpg) (http://www.chillheimer.de/Fraktal/content/Parallel_combo.jpg) 3d is cool.. but the surface of the 2d-mset still seems to be relatively uncharted territory. lets change this! Please respond if you find this helpful and I will upload other, more complex examples.. update may2015: timothychase did an awesome morphing video that does what I try to describe here in an incredible videosequence: http://www.youtube.com/watch?v=TzE-XDebDog Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Kalles Fraktaler on October 11, 2014, 11:50:46 AM Nice, please show a more complex example :)
Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Chillheimer on October 14, 2014, 01:21:25 PM Okay, one more..
dl this for higher resolution: http://www.chillheimer.de/Fraktal/content/branch_compilation.jpg (http://www.chillheimer.de/Fraktal/content/branch_compilation.jpg) Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: cKleinhuis on October 14, 2014, 02:05:25 PM nice, would be cool to see an illustration of the "morphing" features as well, e.g. 2 pathes from a starting location explaining how the morphing can be used
how did you map the farther zooms? by hand ?! Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Chillheimer on October 14, 2014, 02:36:38 PM nice, would be cool to see an illustration of the "morphing" features as well, I don't understand what you mean by "morphing".. e.g. 2 pathes from a starting location explaining how the morphing can be used Isn't that exactly what I was doing?2 different paths, showing how they affect the "same" structure.. how did you map the farther zooms? by hand ?! you mean colour mapping?yep. lot's of trial and error. If there is a way to do this automatically, I'd love to know.. Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on October 14, 2014, 06:40:20 PM I don't understand what you mean by "morphing"..Isn't that exactly what I was doing? Just watch https://www.youtube.com/watch?v=iF-eJO28gko and notice how the shape of the embedded julia changes. This is called julia morphing, or morphing in short. Although I think it's a too general word, because shifting the start point in the real/imag plane is also a kind of morphing. Which is (confusingly) called perturbation sometimes .... Naming stuff brings pain, sometimes pictures or videos work better. Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on October 14, 2014, 09:25:34 PM Short image tutorial on shape stacking. The paths intertwine! Do compare the end results and how they came to be. For experts, jump to the end and find the zoom path that was used down to e57. Good luck everyone. :D
(http://i.imgur.com/bykOIW2.jpg) ...zoom, zoom, zoom, morph those shapes, decrease color density by 50% .... (http://i.imgur.com/8u75x0p.jpg) I made a small mistake in the order of the series. Should not be hard to find. Question: where should the wrongly placed image be instead? Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: cKleinhuis on October 15, 2014, 12:00:54 AM super nice, thank you, this i am going to talk about in the artsy-fartsy part of my youtube show ;) the gallery
very nice pictures, the video is aweseom, deep zooming really rocks da house! Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Chillheimer on October 18, 2014, 01:38:53 PM thx for clarification!
I didn't know that the technique even has its own name.. shapestacking.. It's so much fun to be able to actively shape your results, instead of just zooming in randomly. Maybe you have the multipicture in a higher resolution? I'd love to take a closer look.. Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on November 10, 2014, 10:34:51 PM :tool:
Bump ... This guy on Deviantart really likes to morph, making frog-like structures. Thought I had to share this: http://stevi0d.deviantart.com/ Some examples: (http://th07.deviantart.net/fs49/PRE/i/2009/183/6/5/Sea_Slug_by_Stevi0d.jpg) and (http://th07.deviantart.net/fs70/PRE/i/2010/053/9/4/Mandel_Tentacles_by_Stevi0d.jpg) Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: cKleinhuis on November 10, 2014, 10:41:53 PM wau wau waz
hehe, i meant wow wow wow this is so nice to see people extending the ideas by using them woah, especially the last one is looking at me ;) Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Chillheimer on November 19, 2014, 10:21:36 AM I did a short zoom movie that shows how shapestacking works a little better than still pics:
https://www.youtube.com/watch?v=JxkNEvcU8cY in the picture below you see the stacked previous path very close to the minibrot. I find it fascinating, that even the number of shapes stays the same after each bifurcation. for example, I zoomed past 17 snake-shapes.. still 17 close to the minibrot.. Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on November 19, 2014, 05:40:18 PM Maybe you have the multipicture in a higher resolution? I'd love to take a closer look.. A bit delayed, but here : http://www.rijckaert.org/jeroen/fractal/innerworkings.jpg Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on May 09, 2015, 09:14:58 PM Main PC crashed. Bought new MB and CPU, but crashed again. Now on laptop from work, but only M$ Windows and kinda locked down. So since I cannot install a damn thing, I'm only using third party software which runs without installing (the local IT guy at work is flexible ...). Sooooo, back to Kalles Fraktaler instead of Mandelbulber.
Dove into some low-level Julia morphing, trying to get as much variety without zooming very deep. At the moment I really like those "closed" shapes which spirals can make. This gives the illusion of bounded shapes, for example those frog like structures in the post above. (http://img02.deviantart.net/a62f/i/2015/129/2/1/odd_legged_spiral_square_duck_heads_by_jeroensnake-d8sqwg9.jpg) Source: http://jeroensnake.deviantart.com/art/Odd-legged-spiral-square-duck-heads-532013769 Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Kalles Fraktaler on May 10, 2015, 10:10:41 AM Looks good!
Have you tried to use "show inflection" to help you decide where to zoom further into a nice location? Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on May 10, 2015, 11:06:40 AM No, but I did start to use "Find Minibrot" to skip some manual clicks. But depending on location, this does not always work. Sometimes the software thinks it find a center, and happy goes zooming further ... but it's not on the actual center. I will pay attention next time, to remember the type of locations where this happens.
Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: PieMan597 on May 10, 2015, 01:39:25 PM I find that the auto zoomer fails when the spirals on screen have a higher iteration count than the "center" you want. I think that the zoomer just zooms into the highest iteration.
Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on May 10, 2015, 05:02:22 PM Well, in that case I think the Mandelbrot-center-finder is not compatible with my current zooming method for Julia. I like high contrast between dense and sparse areas. Things like this:
(http://i.imgur.com/iFYPZxR.jpg) This is just the half of the two-fold symmetry. The actual center is the small circle on the bottom-middle. With the Mandelbrot-finding function it zooms in on the leftmost dense spot. Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on May 16, 2015, 11:09:08 AM These past few weeks the focus was on creating low level julias. Each time I more or less followed the following steps:
- Zoom into the Mset just a little to find a minibrot - Zoom into a valley of choice to get interesting spirals (these lead to nice bounded shapes deeper on) - Find a Julia without zooming too deep - Start Julia morphing, each time on the new two-fold shape - Never go to far away from the center for each new two-fold to morph All raw fractals found and rendered with Kalles Fraktaler 2.7.9 at something like 7200px wide. (http://i.imgur.com/i9N9mYe.jpg) (http://imgur.com/i9N9mYe) (http://i.imgur.com/PxGOJHG.jpg) (http://imgur.com/PxGOJHG) (http://i.imgur.com/hbTfGsu.jpg) (http://imgur.com/hbTfGsu) (http://i.imgur.com/h3V0Xne.jpg) (http://imgur.com/h3V0Xne) (http://i.imgur.com/jsL4erk.jpg) (http://imgur.com/jsL4erk) (http://i.imgur.com/igSMYVa.jpg) (http://imgur.com/igSMYVa) (http://i.imgur.com/hEJltUP.jpg) (http://imgur.com/hEJltUP) (http://i.imgur.com/61dP28l.jpg) (http://imgur.com/61dP28l) (http://i.imgur.com/V8ZDer7.jpg) (http://imgur.com/V8ZDer7) (http://i.imgur.com/WVdtnla.jpg) (http://imgur.com/WVdtnla) (http://i.imgur.com/6uvYHpV.jpg) (http://imgur.com/6uvYHpV) (http://i.imgur.com/gmW0VSx.jpg) (http://imgur.com/gmW0VSx) (http://i.imgur.com/n05X2Ax.jpg) (http://imgur.com/n05X2Ax) (http://i.imgur.com/TeIhorw.jpg) (http://imgur.com/TeIhorw) (http://i.imgur.com/85q9SC0.jpg) (http://imgur.com/85q9SC0) (http://i.imgur.com/1MIGISQ.jpg) (http://imgur.com/1MIGISQ) (http://i.imgur.com/ooZ3vRW.jpg) (http://imgur.com/ooZ3vRW) (http://i.imgur.com/0aBymC2.jpg) (http://imgur.com/0aBymC2) (http://i.imgur.com/RYTlQ1v.jpg) (http://imgur.com/RYTlQ1v) (http://i.imgur.com/GJ7BNlp.jpg) (http://imgur.com/GJ7BNlp) (http://i.imgur.com/BWCP3iQ.jpg) (http://imgur.com/BWCP3iQ) (http://i.imgur.com/8oEAaPS.jpg) (http://imgur.com/8oEAaPS) (http://i.imgur.com/mKWD3uB.jpg) (http://imgur.com/mKWD3uB) (http://i.imgur.com/W6VJpGs.jpg) (http://imgur.com/W6VJpGs) (http://i.imgur.com/bHrUt7B.jpg) (http://imgur.com/bHrUt7B) (http://i.imgur.com/XqvGGhO.jpg) (http://imgur.com/XqvGGhO) (http://i.imgur.com/EyhpNAR.jpg) (http://imgur.com/EyhpNAR) (http://i.imgur.com/7eU4SX6.jpg) (http://imgur.com/7eU4SX6) (http://i.imgur.com/kfntkE7.jpg) (http://imgur.com/kfntkE7) (http://i.imgur.com/AphRZHl.jpg) (http://imgur.com/AphRZHl) (http://i.imgur.com/76KyWDF.jpg) (http://imgur.com/76KyWDF) (http://i.imgur.com/p0rR4tZ.jpg) (http://imgur.com/p0rR4tZ) (http://i.imgur.com/yXk8j1o.jpg) (http://imgur.com/yXk8j1o) (http://i.imgur.com/8hlBWAO.jpg) (http://imgur.com/8hlBWAO) (http://i.imgur.com/SLYgBPD.jpg) (http://imgur.com/SLYgBPD) (http://i.imgur.com/vEEKfaf.jpg) (http://imgur.com/vEEKfaf) (http://i.imgur.com/U3gobr0.jpg) (http://imgur.com/U3gobr0) (http://i.imgur.com/OuRgJ37.jpg) (http://imgur.com/OuRgJ37) (http://i.imgur.com/7iOk2wq.jpg) (http://imgur.com/7iOk2wq) (http://i.imgur.com/aHzC6Zi.jpg) (http://imgur.com/aHzC6Zi) (http://i.imgur.com/NETSqgE.jpg) (http://imgur.com/NETSqgE) (http://i.imgur.com/fyqtFWD.jpg) (http://imgur.com/fyqtFWD) (http://i.imgur.com/laeRZhZ.jpg) (http://imgur.com/laeRZhZ) (http://i.imgur.com/B8dAwu5.jpg) (http://imgur.com/B8dAwu5) (http://i.imgur.com/nCVhKGt.jpg) (http://imgur.com/nCVhKGt) (http://i.imgur.com/RbpUtv2.jpg) (http://imgur.com/RbpUtv2) (http://i.imgur.com/rCiZoSo.jpg) (http://imgur.com/rCiZoSo) (http://i.imgur.com/IcIuDAC.jpg) (http://imgur.com/IcIuDAC) Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: quaz0r on May 16, 2015, 04:17:09 PM nice work :beer:
Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Kalles Fraktaler on May 16, 2015, 05:35:24 PM :wow:
Did you use "Show inflection" at all? Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: youhn on May 16, 2015, 06:20:44 PM No, I more like to plan some kind of method or principle and dive in using that in mind. I think show inflection can't show multiple morph steps ahead, so that's why I don't use it.
Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: Kalles Fraktaler on May 16, 2015, 06:26:38 PM The auto zoomer does try to find the center by mirroring parts of the view and select the position where it gets the lowest error when comparing iteration values per pixel.
However in dense areas there can be a huge difference between pixels, that destroys this method. Maybe comparing rgb values in the image would be more reliable also for dense areas Title: Re: Guide to the Inner Workings of the Mandelbrot-Set 1 Post by: jehovajah on January 02, 2017, 10:16:41 AM http://m.youtube.com/watch?v=9gk_8mQuerg Nice introduction , but not sure he correctly ascribes the origination of Bhuddabrot . |