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Elephant spiral tiling with central transformation
By DinkydauSet   |   Watch
12 7 432 (1 Today)
Published: May 26, 2017
Mandel Machine, Mandelbrot set

The whole thing is a tiling. In my previous tiling image "Triangle tiling with layered julia morphing" I attempted to make the best suitable julia morphing to be inside a tiling. An important aspect was that it had to connect to the tiling in a visually understandable way. In this image, however, I transformed the tiling itself. I'm using the word transformation for something I would usually call a julia morphing because what I've been morphing here looks more like a tiling than your typical julia set.

The result is something that kinda looks like a cross. Originally I wanted to make a tree-shape. It's something that I have wanted to do for quite a while but there are some obstructions:
1. Transforming a tiling shrinks it by a factor 2 with each transformation. For it to be screen-filling, the initial steps to build the tiling need to be done twice as many times, doubling the required depth. Reaching the desired result of a transformation already requires 1.5 extra depth normally, so each transformation requires 3 times the depth in the tiling situation. That is a very significant difference that gets bigger and bigger as the number of transformations increases. Depth is a problem because it's harder to reach and render at much greater depths.
2. The size of the tiles becomes too small to see them properly after too many transformations.
3. Currently my best idea to do it is this: I know how to make a tree out of a julia set, so I need to make a julia set out of the tiling first. It needs to have enough details to be able to build a tree out of it, requiring equally as many morphings as the number of times new branches split off the center of the tree. It means the number of transformations to build the tree is double that, effectively increasing the depth by a factor of 3^2 = 9 (!!) for each extra increase in number of arms. You can imagine how much larger 9^n is than 1.5^n (n being the number of transformations), as would be the normal depth increase when making a tree. Without any improvements to this, the idea is impractical.

I've said something about making a julia set out of a tiling. The way I was going to accomplish that is by doubling the center of the tiling, the doubling the morphing, doubling that etc. which results in something that, for my intentions, is similar enough to a peanut julia set. It just doesn't have (infinite) self-similarity. What you see here is an early phase of that idea, doubled for 4-fold rotational symmetry.

Magnification:
2^9870
1.4657408896420228648538645519085e+2971

Coordinates:
Re = -1.7498439088634276800460948042342922498295334226571513188740914298952160154495160835921441755475654893999982369876215851617592098468229564680702922351168965760097475776102438594727651509787077718910539436125381937707617605884622639199601316173201755267877495940801859921008741036365835317535325754579310659698172718927559068739259993943489903422220415937003111035235632482550767932444453657416776260831329826364139257446420512980873151922763831367430838804091679690611736967486334921632295099429770359931163075192348893492407688808513153245277731668770979345334874317532468385607661936063534917048525309601960566949936316979336866617749321597297823714013372646899964899346285783803172833516418670799966711933325159465508213919277200803000055872852120819029687577982703573729797193182111971306136776267365805118136976570306298588531306446692744199554252596954263700577089578723507789675760521447513869517740980613852561229822340340821960377577072823654587832275540464160845654172941864633386678150003773464150372439849205478866686753163400567627899379488621753733939322237710510489899894319695620114081220960799108362857739101378201141015236614994736212399978478462228663563168926677891397591332060282422583766336444493991592761516899516720428428445030542837098451502818031894096231891126049834098808975971389759975985150362816201102121018083628059439863570774916034325209057641891673750907649855902580808823385917908184577563638857597924200360805831466148522376361731640904864693988420015313810216766041336750368569166250692222461154246966278977859304313592575028322631156576324942021305183391989500220481100230016404570236474879345415061504192883601549161673363117250118782954658561767077600417297183475910010828666415715253229639189256362950223239974866161213210866713886300308480188590857334497621417446574144421055762236175453201119570339202660482102753858422401131043468838188246221038734014328251300488439192100059396153720293433575490048680511435309255321529303432822265191296671629725830605376213014511810829167186060245587406244714168349595569030001662916290777088899112276716205440876804982372349280290334339551559023028248022816778418359021526473978858832783517847281048800951679546036790338353953143256548965295380780837896255691843446714391071948040002697770654394052015260255393376175280788923261119479110963358582732044643161872472885492978505953850286721671320296384955791562868032502403710449580790524128525636701394699880064688726954218490244554281678600023139268604824255407806421895967872781732308596780588474743680047670637781940624315346439381802681954581244045582241975959875957962316604643837152815035116622127450845860253963974889814159946447197039023379170539609194628016770286801768992266381824648034095425613913539495478717100958571514945248496902412048555941047782774510767649781516106282821761253790079756292170876360361748187034655726742995944555407678379822885287868173604717194566230010229214603428202446987503287921106362107355612486404563715497

Im = 0.0000000159959473146319642717540099365976948500705065715209798252640461993465538628308271291417567856676375259782625663886020914208896933202641339653886737470769520025797007857355688277340916809887701394149355736780982888336303707426011948432980348233270700327920071207166294721964801722915416135341446136599969054710440421562301919810640516949611055655445374278378523875044932672841451066063600543720534132018364998118432787011667094357767592746119445662386613217689596616495795570879453511631475015465202878892577516514921740593502750764153271780790082960896474165423118429738903206147242877552749256873871105093358252352732331060728483105073241167843748437518392524351874358787417493003841145166331703983481875389753117117932032962953506584753054080076767788009823281476265482712320371045802342552403470963012571639687849320512232492175287872997902858556379366234132626695909943079162218988205311016002657446116689747111210533111481206942309139308952184605691152141960826333395982721345476132751975971022146535204595433352512002578302892490105214373912229371581958063660115836891169373147116580207143925553002261364624545240328038200540148829737033585513962225949452826609947213453364282239248466862885661935973676913754680865468875965089162465135074498164822314446163324863073935405497487064708583916816516533975726680127663202426511499033222075508877083212530649296209358665321153111812420249785544611998025674846336691047595198408371194264939589594429132157351553726174718486809904515040993978014361545147263981626591617347758542367019696332480685643916496305189291127422116306514284473360959979610585543698541400957830806278941724934040493095816324802704019794878310546321765246167763900378695196267121408050678909760576027231496049406396550408670379362262182178544798472264457901620793091459280836757386717166694446359647130402178640031711905205225841807086759410586590898742578188102841587698798631546687215830493331902873137159054492715093065045167280084467604666680883585150536344069812477725101393596817253505556349472358259816524030849996642801406956427167170327092676365024688733492601876964692824759894626974050081365969753000708139172781769560750226186916342763822262989132793630073189830957326040774791732039169455213647452293020342005664871046362252739644996046672804407485968984950340837280695544530862471085846992558012998912101664588802674745392701373309979629845938837179272067628387974487488874154567647656115499120884893301050640923839135312465224721530140263802091571317219010359968405330584283214583937484038726235020015489667750541678639777104491176726074347886713693804393387049866338689190684271772913934340107566951726283444179319632633810736907114231121232694263979534185977644430817648323272004289857100248104618629806930539306672302326896495469553220010205700230257475740272421099410035434715924022827075312970916872859580939642662854699129713633533001625605559242928706357843554207880763875716758293274507690637883513572704426297634947130620506
Image size
4632x4632px 42.55 MB
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Comments7
anonymous's avatar
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bryceguy72's avatar
bryceguy72Hobbyist Digital Artist
Wait, just to be clear... this is a pure Mandelbrot render, right?  No polar-to-rectangular or hyperbolic transformations or other image manipulation, right?  You found this area by understanding how the apparent Julia sets transform after repeated zooming into the Mandelbrot set.
DinkydauSet's avatar
DinkydauSetHobbyist Digital Artist
Yes, that's right.
ADAPTERR's avatar
OMG you have sooo cool ideas! :) (Smile) :) (Smile)
FractalMonster's avatar
Absolutely marvelous :omg: :wow:
DinkydauSet's avatar
DinkydauSetHobbyist Digital Artist
Thanks!
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