Title: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 06, 2017, 03:02:59 PM (https://pre00.deviantart.net/d994/th/pre/f/2017/270/9/0/3rd_order_evolution_of_tilings_by_dinkydauset-dbmkafg.png) (https://dinkydauset.deviantart.com/art/3rd-Order-Evolution-Of-Tilings-703026124)
EDIT: I have changed the image to a new version. The previous version contained some glitches. Right now it should be completely free of glitches! I also changed the anti-aliasing algorithm to prevent some of the Moiré effects caused by the fine tilings. fractal: Mandelbrot Set Computed with Claude's GMP fork of Kalles Fraktaler KFB map converted to MMIT with my KFB to MMIT converter Colored in Mandel Machine with a custom gradient designed in Photoshop Because of lack of inspiration for new renders, I'm currently dealing with my backlog of ideas that require extreme render times. I have been since early this year, actually. Most of my ideas since last November came within a few days. This is my deepest render ever, made possible by the further development of programs that render the Mandelbrot set using perturbation and series approximation. The overall shape is the same as that of Dragon (Deep Version) (http://www.fractalforums.com/images-showcase-(rate-my-fractal)/dragon-(deep-version)/) except that this has 3 blobs with shapes connected to each "knot", instead of 4. Another, more crucial, difference is that the shapes here are custom, which requires more zoom depth. Applying evolution to 3 different shape types severely restricts the number of morphings that can be done per shape, unless you just zoom deeper. That's why this had to be so deep. The first shape type is a Golden Ratio Tiling (http://www.fractalforums.com/images-showcase-(rate-my-fractal)/golden-ratio-tiling/). The second shape type is a Hyperbolic tiling (http://www.fractalforums.com/images-showcase-(rate-my-fractal)/hyperbolic-tiling-with-golden-ratio-tiling-pistil/), which (like the fractal that the link leads to) also has golden ratio tiling "pistil". The third shape type is something different that I haven't made before. The surrounding tiled bands are highly rotational symmetrical copies of the initial repetitive zoom path that the tilings inside the main shape are also made out of. Magnification: 2^27847.24 7.17440059980 E8382 Location: Code: Re = -1.75692634460316160675134394766835104834943441352722029912924065902241784829151216850143527294619071001178323194406484336615754964552055784461008727849817917268371626136140599175636738612440325884863721246308936374409171932528434497619519693752587870348434070650986841980378510816842390613737970309262934653068551039674547470192116133561631426623115895368000359988994486540354868232367870370876085180165013912410139954981758328125234223346412083583005699792181521736593106820888667060541181763493465558665712131250460983649174494025802761822118394583015643998170572936824460397953936193622430635560906464968775124477875340679002868712329324847450746752553848117766270652400662385766907028585897038377025909544489606724703289385005176210182321151206424315055186374058006818832317808849748961572244175653736174783857839169016318359302697449907424159438330953913330877210770375885601239417271948026655885587086874461409819278090362421154144130691678174317753040966697017498301404580997972696222901716137325164413291067384211404193332482891682992721177146968154171558811515355088235559133077310675400682520137137074488436016863311458401905624276423802972748904751180006345918802953846638357341640528967864650015533544004667982604354015271232307748145472918687466881598862130731978527005596620611083846393868360598473092372242399977762170481418166294250485615090364643668868210707334409531851756930034050537091329598058375750278329204281124530560955339642770097749792814100207321861879941185091895878368717020899828294209359864430034107702403403388713463411995575238726190077670765421471235443481036849674106515964881636760142207412866808387391739355235920398740984509347925123266725805109853915114744881417310057989407519736028809061525114481664977938893227178869803270316001742274938323687267929337751878084010142375280378806771607033510448402212242878450869643168396157707798154578761792311615815387141349108991000820644960034938102564723128105873287295949004762889910650289101184924259282655044501170088850809423527927803998515940995892516571906069598087643648972510849927689082424530889937560618991863067409256107803891808150636519700571150367263605645951483329485725977609886838355208361243460914221450570291951815813805532390768694916452448422620869445354478339344377195981558712472083946060842445414753374611728323220518215776326952673797162938021293582710371778297747354630977045967544731926475315535208793263167027498561486638626897480386060264887886863213864287542552786430969501889727555620383757987097657500993086728019895646134721283270442866330033235640126280539132417337385475913499717780683289193340803012725425871200931840414027215683689800890506800521185626327249425609819616011346888384754212261881886296389096767061087457607600647613804537701005909862910528036469232012038289583692865452131754330569103626761561144849535707083388689109652702314547811631378215579505587419383975494826705859480175119287814332800530754472062243957013500296369682757108062005029962517255351306861926888885453593641347927657368930274796598455029305853520786750002958304648306485385752245513458621593728274590302596187900158675171568801367257072047325371698217243967569734124747097395956166530236114618584097003028985879579638942904612210561585705691533895290422958938129036716080240311732692756795254073693989502264691510228320104652656500678351161057031291589362873215679871601241400027029957897013458296435036050692646015313096539864166998766647491739304028278899046397301230224903643372195799368316878000968862238018639502131607346355647142749141297327116252408653112032469467947421013915045655217586722737493365483275169097760784108942628243855030028102381914424031295544363607914161431610992338027501925467650409404679491065338907178953441356692498840090175746557113229545968349303501936197847626436682182623452415450005063747556464124327296730041260630462226402789324913240471062685683950967436344585502296846855548374089907516825998133103179847961387193472983925227716928332908959587675645112481181355645422456623413186643908311478940698290224415383257175847760797315763799442553944452495180723290658657353078623545877141012531096734368175853512079189547192578321366460719136146589285778966818271097582921393850427655800097199634636499242225600564180434295160335903435869073006144264290892843661243802324276489606465071784809215083968372713307972931766579686003045023745109148792949714135822344053611767955724724560183043154820688860175801939279645332300406268754078478408596401375296314025296346932349710637922941480789281091611799629612255796006579901845190398301735948719673597040669332751155645346652158722582560554779610092001200730002603247381120237308033716860706720224865609032520214260488111114301919162143296386936381866491347887110641909142314882735082046376871629530550924058573865319901027201433717287778030154010625441501569095808961462511816248068339131973815704800798992765539747124067437193271389637179094611540770902320313060322475569355798107962275719644662144433417475091726092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Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 06, 2017, 11:54:55 PM :wow: Simply Amazing!The surrounding is fantastic rather than the dense stripes that is common in such deep images! I am not able to see the misformed parts in this view? There is one issue that has been revealed lately that may occur when doing very large resolution, that when the number of terms used in approximation exceeds 100 it is possible that glitches are missed. When that occurs the result is that the end points of the pattern becomes blurry, but this seems not be the case with this image. I think we should ask Claude to limit the number of automatic terms to something like 60. Edit: the bold marked essential words were unfortunately missed... Title: Re: 3rd Order Evolution Of Tilings Post by: claude on September 07, 2017, 04:21:25 PM Beautiful and incredible!
I think we should ask Claude to limit the number of automatic terms to something like 60. Not wanting to hijack this thread, let's discuss it on the new forums here: https://fractalforums.org/kalles-fraktaler/glitches-with-high-order-series-approximation-used-for-large-images Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 07, 2017, 06:14:30 PM Thanks for your replies
The glitches are small and look like the result of a regular julia transformation. Here they are encircled: (https://i.imgur.com/7U37C3y.png) Both should have been round, but they look morphed for some reason. It almost looks intentional, but it wouldn't be possible to do this normally without affecting the larger embedded tilings such as the one in the center. Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 07, 2017, 11:05:40 PM I am sorry I haven't registered on the new forum yet..... :embarrass:
In function CFraktalSFT::CalculateApproximation I caluclate the number of terms to be used, between the thumb and index finger, to Code: if (m_bAutoTerms){Code: if (m_bAutoTerms){Which means, unfortuantely, that less iterations can be skipped by approximation, and that render time will increase... Title: Re: 3rd Order Evolution Of Tilings Post by: claude on September 08, 2017, 03:26:05 PM a condition that it is not greater than 60 would help a lot Thanks, I implemented this change, but in my test glitches are still there (albeit reduced) :( Will try increasing the probe point count when I have time next week. Title: Re: 3rd Order Evolution Of Tilings Post by: hapf on September 08, 2017, 05:37:14 PM What is the iteration range of the image? How many references?
Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 08, 2017, 09:15:37 PM Lowest iteration count: 32 477 267
Highest iteration count: at least 32 543 000 There was only one reference. I can't determine the highest iteration count exactly because some pixels are at the max iteration count, which I think is because they were not computed yet. I should explain. The render didn't even finish. I rendered it in a virtual machine and saved it every 10% and at 95% and 99%. After reaching 99%, the program crashed at some point (probably when it was at 100%), so I went back to the saved 99% state. I exported the partially finished KFB map and decided to work with that. I'm not entirely sure what would have happened if the program didn't crash. Normally it hides glitches from view, but I can see them in KF's window, so I don't think another reference would have been used to repair them. I also tried convincing KF.exe that the map was the one and only frame of a zoom video, because there's a glitch reparation tool for zoom videos (file -> Examine zoom sequence), but that didn't work. The program crashes without a warning. Oh and by the way, Claude's versions always crash when I try to use the glitch reparation tool, with this error message: Quote Assertion failed! Program: <path>/kf.exe File: fraktal_sft/CDecNumber.h, Line 124 Expression: ! (b.m_dec == 0) I also looked more closely at the glitches and it appears this is actually a case of the blurry glitch. It's just not very apparant with my coloring and 5×5 anti-aliasing. Here's a screenshot of the largest glitch without AA and with Mandel Machine's default settings (much denser gradient): (https://i.imgur.com/QI1INtj.png) Title: Re: 3rd Order Evolution Of Tilings Post by: hapf on September 09, 2017, 09:30:31 AM You need a couple references more to avoid the glitch. What skip did you use? Looks like a place where a lot can be skipped. At this depth you use extended (long) doubles for the iterations?
Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 09, 2017, 12:59:06 PM I don't know. Kalles Fraktaler decides how many iterations to skip and which datatype to use.
I had "approximation low tolerance" unchecked to reduce the render time. In a test it seemed like it made such a drastic difference that I didn't consider leaving it checked (and in that test I didn't notice the glithes). If that's what caused the glitches, it means it was either no image or this faulty one. So it appears that even today, rendering at a depth like this is extremely hard. Finding the location was also a pain, even with Newton-Raphson zooming. It's easy to forget what to do next if you have to wait hours or even days, and it's easy to lose track of where you are while zooming manually (where that is still required) if rendering a small preview takes more than an hour (including reference). I kept the plan, along with the coordinates and depths of the minibrots found, in a text file so I wouldn't forget what I had to do and where I was. Also I kept screenshots of the test renders with annotations. Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 09, 2017, 11:37:26 PM Yes indeed it is hard to get there even today, but it would be impossible some years ago :)
The unchecked "low tolerance" is also a factor that can cause glitches, together with the number of terms. For this depth the datatype used is floatexp (a double for mantissa and int for exponent). In principle it would be possible to use scaled long double in the same way as scaled double and that would make it possible to use long double up to e9800 instead of currently e4900. I think that would be easier to implement for Claude now when long double doesn't require a separate dll compiled in another compiler (gcc) Title: Re: 3rd Order Evolution Of Tilings Post by: claude on September 12, 2017, 04:27:39 PM I also tried convincing KF.exe that the map was the one and only frame of a zoom video, because there's a glitch reparation tool for zoom videos (file -> Examine zoom sequence), but that didn't work. The program crashes without a warning. I add debugging this crash to my TODO list. Claude's versions always crash when I try to use the glitch reparation tool, with this error message: That is to prevent a division by zero, which would also crash with a possibly less informative error message. because GMP big floats don't have infinity/nan (unlike MPFR which is more IEEE-like). I could make x/0=0 for all x, but that may simply mask errors that should be fixed elsewhere. I'll try to debug this to find out why it wants to divide by zero. Added to my TODO list. In principle it would be possible to use scaled long double in the same way as scaled double and that would make it possible to use long double up to e9800 instead of currently e4900. Added to TODO list too. Title: Re: 3rd Order Evolution Of Tilings Post by: claude on September 13, 2017, 05:56:53 PM Setting x/0 = 0 in CDecNumber seems to allow "examine zoom sequence" to work, provided there are at least 2 images. There is a logic bug around https://code.mathr.co.uk/kalles-fraktaler-2/blob/refs/heads/formulas:/fraktal_sft/main.cpp#l2200 that reads out of bounds memory (->crash) when there is only 1 image, I need to try to understand that code and maybe rewrite a lot of it. It's a bit too tricky for me to solve today, and I am busy in the coming days, so I hope you can wait a little longer.
Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 13, 2017, 09:01:37 PM Of course. I expect nothing so everything is a bonus.
Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 14, 2017, 02:11:07 PM Setting x/0 = 0 in CDecNumber seems to allow "examine zoom sequence" to work, provided there are at least 2 images. There is a logic bug around https://code.mathr.co.uk/kalles-fraktaler-2/blob/refs/heads/formulas:/fraktal_sft/main.cpp#l2200 that reads out of bounds memory (->crash) when there is only 1 image, I need to try to understand that code and maybe rewrite a lot of it. It's a bit too tricky for me to solve today, and I am busy in the coming days, so I hope you can wait a little longer. I have assumed that there would be a full sequence and not a single image.So I use the zoom of two images to calculate the zoom size. Once I wanted to fix a single image, then I copied the kfb file and renamed it to what it would have been named if it would be a zoom sequence. The CStringTable class will return an empty string and not NULL if out of bounds, however strrchr will return NULL. Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 15, 2017, 09:11:31 PM Thanks. I have been able to examine a "zoom sequence" consisting of two copies of the kfb file. I will see if I can use this to fix the glitches, but not right now. I don't have enough RAM available.
Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 16, 2017, 02:27:23 AM I was able to load that zoom sequence with Claude's version (20170713 to be exact). It can also be loaded with kalles fraktaler 2.11.1. The eraser (which is a huge fixed size rectangle) can be used to erase a part. However, clicking inside the erased part (or anywhere else) doesn't do anything. No reference gets added.
I tried doing the same with a small test zoom sequence with resolution 640×360, rendered with kalles fraktaler 2.11.1. I could examine it in kalles fraktaler 2.11.1 but not with Claude's version. I also rendered a similar zoom sequence with Claude's version. I couldn't examine it with Claude's version itself, but I could with kalles fraktaler 2.11.1. So Claude's versions can't examine their own sequences, but they can examine my fake sequence of 2 big renders, for some reason. Anyway, with the small test zoom sequence loaded in kalles fraktaler 2.11.1, I could erase parts. Adding a reference inside an erased part turns the erased parts (all of them) into a different (though the same for each erased part) color. Adding a reference elsewhere in the image turns the iteration band into a different color (that's what it looks like). Changing the main reference turns the whole image into one color. This is what it looks like after a few extra references and erased parts. In this case extra references turned things black and erasing turned things purple but it's not always those exact colors. (The black inside the julia set is a glitch.) (https://i.imgur.com/BT7K4Tg.png) Could it be that other parts of the program changed, affecting examine zoom sequence without anyone noticing? I don't remember seeing this weird behavior that one time, a few years ago, when I used the examine zoom sequence tool to repair an actual zoom sequence. Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 16, 2017, 11:18:57 AM The size of the Eraser is the same as the rectangle you get from zooming by holding Control and clicking - Action->Zoom size
When opening the "examine" function, you choose a kfr file, where the location parameters are stored. The program assumes that the this location is the exact location of the first kfb file, and the following kfb files are following from that. The zoom size is calculated from the file names that are assumed to have the zoom depth after the underscore. I am sorry this function is not more intuitive... Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 16, 2017, 01:19:21 PM Okay, about the rectangle size, that's good to know.
Then the conditions you mention are met, so I don't understand what's wrong. I wouldn't be surprised if only the fake zoom sequence wasn't working. It's just an experiment. But the zoom sequence I rendered using kalles fraktaler 2.11.1 itself is showing this weird behavior. The kfr file and the file names are generated by the program so they must be the correct format. I assume by choosing a kfr file, you mean the one that is saved by the program before rendering starts. Title: Re: 3rd Order Evolution Of Tilings Post by: Kalles Fraktaler on September 16, 2017, 03:53:57 PM Okay, about the rectangle size, that's good to know. Yes, the one saved when the render starts, which have the exact location of the first kfb file...Then the conditions you mention are met, so I don't understand what's wrong. I wouldn't be surprised if only the fake zoom sequence wasn't working. It's just an experiment. But the zoom sequence I rendered using kalles fraktaler 2.11.1 itself is showing this weird behavior. The kfr file and the file names are generated by the program so they must be the correct format. I assume by choosing a kfr file, you mean the one that is saved by the program before rendering starts. Title: Re: 3rd Order Evolution Of Tilings Post by: claude on September 19, 2017, 09:50:19 PM I fixed some bugs with the examine zoom sequence (thanks to Karl for the pointers) in the latest build, kf-2.12.1 at https://mathr.co.uk/kf/kf.html
I haven't tested the glitch correction/eraser though. Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 21, 2017, 06:02:06 PM Thanks. Correcting glitches with examine zoom sequence doesn't work on frames that aren't the last, but it does work on the last frame. That's enough for what I want to do right now. If all goes well I will post a new version without glitches when it's done. I don't think I still have the gradient so I will have do to my best to recreate it and it may turn out a little different.
Title: Re: 3rd Order Evolution Of Tilings Post by: Dinkydau on September 27, 2017, 06:27:05 PM Here's a new version that should be completely free of glitches. I also changed the anti-aliasing algorithm to prevent some of the Moiré effects caused by the fine tilings (apparant only in the large version at deviantart: https://dinkydauset.deviantart.com/art/3rd-Order-Evolution-Of-Tilings-703026124). Thanks a lot Claude and Kalles Fraktaler for the help. (https://pre00.deviantart.net/d994/th/pre/f/2017/270/9/0/3rd_order_evolution_of_tilings_by_dinkydauset-dbmkafg.png) For reference, this is the previous version with glitches: (https://pre02.deviantart.net/9015/th/pre/f/2017/249/7/5/3rd_order_evolution_of_tilings_by_dinkydauset-dbmkafg.png) Settings used for glitch correction: 48 terms approximation low tolerance OFF like before (otherwise the correction would have taken as long as the whole render) 2 Extra references were required, and the glitches left by the first additional reference were detected. Also the small number of unfinished pixels left when I exported the map at 99% done were rendered, which makes the result exactly how I originally wanted it to be (notice that the new version is slightly wider). |