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About Digital Art / Hobbyist Dinkydau Set23/Male/Netherlands Group :iconmandelbrot-portraits: Mandelbrot-Portraits
 
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Newest Deviations

Triangle tiling with layered julia morphing by DinkydauSet Triangle tiling with layered julia morphing :icondinkydauset:DinkydauSet 8 3 Elephant waves by DinkydauSet Elephant waves :icondinkydauset:DinkydauSet 8 3 Sequence evolution by DinkydauSet Sequence evolution :icondinkydauset:DinkydauSet 5 0 Dense deformed trees by DinkydauSet Dense deformed trees :icondinkydauset:DinkydauSet 8 3 Hyperbolic tiling with golden ratio tiling pistil by DinkydauSet Hyperbolic tiling with golden ratio tiling pistil :icondinkydauset:DinkydauSet 8 0 Hyperbolic Tiling by DinkydauSet Hyperbolic Tiling :icondinkydauset:DinkydauSet 6 0 Spiral path morphing by DinkydauSet Spiral path morphing :icondinkydauset:DinkydauSet 9 0 Golden Ratio Tiling by DinkydauSet Golden Ratio Tiling :icondinkydauset:DinkydauSet 9 0 Dragon (Deep version) by DinkydauSet Dragon (Deep version) :icondinkydauset:DinkydauSet 10 0 Density near the cardoid by DinkydauSet Density near the cardoid :icondinkydauset:DinkydauSet 4 0 5th order Evolution of evolution (model) by DinkydauSet 5th order Evolution of evolution (model) :icondinkydauset:DinkydauSet 1 0 Dragon (surface version) by DinkydauSet Dragon (surface version) :icondinkydauset:DinkydauSet 4 0 Trees Revisited by DinkydauSet Trees Revisited :icondinkydauset:DinkydauSet 8 7 Polygonal partition by DinkydauSet Polygonal partition :icondinkydauset:DinkydauSet 8 1 DeepDream Mandelbrot by DinkydauSet DeepDream Mandelbrot :icondinkydauset:DinkydauSet 3 3 Festoon by DinkydauSet Festoon :icondinkydauset:DinkydauSet 6 2

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Activity


Triangle tiling with layered julia morphing
Mandel Machine, Mandelbrot set

This is somewhat like my render "Golden Ratio tiling" except there are triangles instead of squares, roughly, and there is a morphing at the center that is connected to the tiling. Notice how the tiling looks odd close to the sharp peaks. This image shows what a julia transformation can do to the plane.

Magnification:
2^7561.284
1.4903550178318449484728738200504 E2276

Coordinates:
Re = -1.25539673868026755865583057881474899884324965805338977974834931161909270753708598428507955786132265725790787341032505996383790425294770009682926760678760038756350899655215102205878644724210739492794886576603695584822056326228944405322883876128043521419784068398650048082189903328094223666928063926518382846840131859485476315478235880711721658003833441256818569046853194430529350784682119536773108833463488393163697761402192429756097387714961858678744874458199522006130576804388906748570341814504336685457587167749548288322872130218471448274839817042698717905831296282896184572296128713908967449798472116056514881888801683939223851000287431323336894442496881378705777070710371054440806027399735639396692322947494320719306470574708085702346217592836955660079971867889777798610664668864742574634950499717744718773283207042687948226229603847906214983193112664398233916204454147724975238550562547821344963081493668638526943588769755260131804899721402074907287731519191451163524738558324798559761025301908168987100951527274712280617758661403864423907751426459851506821125537839398255354437258208725148760906354197699944849968108933608465947163436828331417300771517124475934726602173762300539357803205221245585415774897112143250119426714150301309801319608451015128386035191726911921409455877878074524972060731613571786401216370540706975177651621092906520896665796647089230257511709648826321414635400998938455772429223454925573977621930697636796075847672588969185212087053053108181349608410897392328263641074037370638422842713171865370885525752501270851054922936215247758843441612554173733605068983133288967390278512576317125435856073016415738023888947607111601785315411777998870973224588870831157000745915650340811818424894326691568333333287310663932565094814901141779668577091589977159231317802556812362499811007994432885830314171973035269633162611613719150560321254470550921982493890373265712289506368372242619429278367534066301408804736183112417208921239690694152920285716471700108933703166679275908879135641167270283866791874989692797333223912642355592898942261239801754647548769348903336461818747933068920743148283632266306881018573511463953740275679828863365826198203134232482131820640409927700991821156544305676637683125693206284943518734414060423813465798754462992799430697523597233

Im = 0.38224857379114731727780160618658277870068837021245609010295408004674654682792434651526067447152075016911712054055366594385153982530268591629940094738282878381005830478368034558265856542451001686964767561086991338229754750137888164432857760503555842214222748025269569910342171779788637618093216751365225088244974732240931656948930320932483314069560030252947914416671414075723933875670577050947611642505633422489719007040329288770428757402243349059412605593643265949963772513244211135482494958912615966962376348986136117109044491259528402746005899258602303394927333974607538059934632921409448592026483942987894561898331313170398847213274560540208498080978196884537151786484867735486753128144430866094488699815209010954095152294908726663605582313599516699642043260982989596201950521373657665888156922245012034452507667911384714233976586046957767863867279164854686440895021022140335576849458186739533079907091119760435026551937347806292204466683044092574239012840186428481524219398943802887008041935819677278927676704522741056396257948015133645827160792737869947636479090032335098323726897300010931435172681809140933116797070843783091397880472133475422388098864490610439426060149139216159026208588057288395717243484806167182597013551312010188295824752786932984887460712578604990706454971450496155631761424072659784071238345487466805278971489867754392033632748812447312563394897601361535407192856390587221545771654081274649187234430101177287585350211747493805773283204901741582650483692607104969109485572537275107060195960439335093314127023513241367490068166620554906791774001717991666159176505400523230151821683091826328729376557926320188766146883076918559315535454082956773400405689949643379087530045232955917580766583998251709877442400316338096059478353544725752163596160773833593059946203114921949849385337925897088224267096835539727189957953695650604725670584459478345615025117820704668603117497969156810146795706772328220444509536691189407404386319819509366133216601247025480866130704549612899154869401996166840596106974136261677011932709383792444954406525867356896445713414748391884204484183065722694821005218717482082087096172332556051444206891571881664322252754694587273228380586639882319729340727003245417557444363395896390486793186299739084951434426861761486920154278237706587
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Elephant waves
Mandel Machine, Mandelbrot set

Magnification:
2^4182.477
1.124690883091685866186702988919 E1259

Coordinates:
Re = -1.74975917037800050882559106905118750347894214705113542310138791588283442362476794679447379697098337897360380421747537132084177320502872411235004407548291182180220013815784315475119718890858259656345535782423842150705516620434263761115431902470969102299880098926517978912243548772936862151476086759300271704388126344726012474333639866928628752210535408485545059595327550722505752203093841907450401826993892093789118576467344955542020395570425414462370414055524690121110917933282128973112601913616234372074060239459335785573755715506635897305574938124965241397942822443513866282490361782964557196272987423432943989613563484609378000234123636460371172469332910496908840112367523249650308846385894020387183664455996071760284596565209943953396746546991668526196540545907704963402114759408854092385724106953664362453122799519641510073320189430787797737692402590502745389320262056722558822620115778743534192455984051258116177551002351462337179828974581234931469341402834449247747148613854365941333373404789508697903427259196456082684107101864376356383411125025541612063313422327656067398776838299189210018921060489815307622553023409775956982585571816789705098897391324969757769978964451887553404728997176032184406315075365024771720926778298394168977346537844147588162605229

Im = 0.00000065494321464889382395974433548871503861114693049267081515861761243775606941335923766366505355757907021252213122344880630973753203925749497175311893412307237560794258013506711204865294085458745997756305392378064184786596023324128022855641754079645576938607519951982259780438763729788334075452120238755072608348553720523565328171546892700838522789925063190670592587502234964120757097262904912008197340907217242063047632748247153144932253629421239182929452834832405234711442216705522169867738484632487692296978366791361910635637442128464391575578753412821439830273798551500960009077448557732252708009579372346725123703729993352767677363408828600982651140875896265497435630538832509926132678178011558566914911752363563027266475171854228449032212224282831660095165993611404467019808433602873368347067095976691348182625375509713461911953891646629928543220165098623138887791782006927265737975906706782192103382769986044941530583462560200703142636177894286413245330140929999169372093753516169686080903702948047663760448820578181151981451428626324919991051944807585171714992242287793310021623618003330578825893164347407043190662280917017920211141450056073171323522898256168810102684391651125295361344625916133328594687384738376690067347633459855395375232360091982145566
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Sequence evolution
Computation: Kalles Fraktaler (Claude's GMP fork)
KFB map converted to MMIT using a KFB to MMIT converter that I made
Coloring: Mandel Machine

This was rendered in 4 tiles of 16000×16000 for a total resolution of 32000×32000. I used custom software to convert the KFB maps (iteration data) from Kalles Fraktaler to MMIT (Mandel Machine's iteration data format). Then I used Mandel Machine to make images of the iteration data. I used Photoshop to assemble the puzzle and apply anti-aliasing. Normally I would mention the main program used to render the image and omit programs that play a small role such as Photoshop for anti-aliasing, but in this case that's not possible. There's not a single program that is clearly the main program behind this image.

This image shows fractal patterns in sequences.

Oh, I almost forgot to say: The bailout value is 2 here. I missed that so much since perturbation was invented. It's the more natural way to achieve coloring in my opinion and I think it's great that Kalles Fraktaler has this ability. Everyone has been using higher bailout values because it helps with perturbation. Before perturbation, eveyrone used 2 because it was the lowest possible bailout and therefore the fastest, because fewer iterations had to be computed.

Magnification:
2^10034.880
6.30995095145 E3020

Coordinates:
Re = -1.76903662721565731264101749028160721190904888023519544905339483009967096815954512652634436154905415591870716847237764013229498980265679267261337975001530618312124578753263934001694377207606864054726220329965296608235526628786340370626765274146681221532084205791351666644520044085645155512564315353491623270200170512021690460781620534374681537676200890850023584032373690206493193949308922079101762557630378717785910568998757879881450589620795124876217302029809542808486175015332369660530964326605097675262605304601499158888494888525650692764205785901544467837783491053218727089288054178869753150950077001099753831649997149191649524864211413476995831753350162357932231007733115563745631411875623695749943519710199998507683085969902371531629120161571088037653898125315154340403422961965389681439145148512338274481798384611284391747887824748941127026237186341970625675693566994917166974583329483208207339772166071377052762418793513738778998744097503148025740856805563260088813197191330664901229880489767413068120967527338708027055681065208173403604018186750103953159354178215660292014712465304818969750902060940604599335630683036999625685759807374788759170487504518049658362030252747600030414495104862639384108620434756170103142687104056859931289625698897448565919164709411338356915335037014173094857998984231614218054992514094749817126718353266709031027855597431047585888356287537980775906601190281176520843528530371122803901835817230437818598856774655814527010524730806213344486706736978506663867905670692547377066426973939081227023125194678102291793913432344599780164968464067896551670792827562382223262670651337922529327820981553916018656619476028562934590703172497345072709370790097614946816161167330363164601395719240071333361735785342547244917686034173389488385443225043525134967010296372001373725563011417627541185139744177173442269532631731813000816201372017961482525193177468768926188903777530171187729144053915866134445951302115777442964129698046266738721161443654604293311737190492251094379113487454688298981289919977731795419700045717526249016543233381471813616990484340610822413509559219467177016553710490127822219337306175506755151287050152333319378768538394768991531748060747649365846250879906159243907716686222986567685509856375219575841753820173024482734961466301652007741380152838463041418555947934104870883099933060435496992668907853058009591628089113094725603315983372382302142884798365396349327394988308347045110648245725287660620602677134662985702018512827295396179849923108422657946742012837566769277577032555491932518454649593819882382065267718483272049083880723517899679081619394549078239880858962721103631975296057628469741222990875851334053249653786470030521615911244978721994419905907372778387799584938262956493770299932933351258157617593659525416356716298117515320541988120760632800525269743243492671595187127448252863247832944097616543148622913500479025829506138971961305859287674906202848536984072112555368221123940999717199954829404052269131115250293576673948513334946579837687078520652507457276118179424838906005
Im = 0.00315510948974492697145473551355899286034321461233687852579200020768847305652212619513913418474795832344439949603068976241632626490296340544369856275169449382958867174477932441624782958704142742430449129316470673628498794184139952850879059533766592649597258366586269319597636749314028031210003647496803674503156269315287035035644109195671097025475282026065557266046865469074860461286230345311216356484777198319498434549749588475970244862829219105211717817003231755641179450633803201932248333053300263373704401566152020561635979277550725198158881685047701096265292092336423987619211834084505768701791793501715766555699809226828761357019535153366389623555878331259916563831917741000173776205627727891086182481882203247049367185436658003287155300045490394511832313068734979624567391164213655445673846139796915317010588665204615033653397772297843747017362287304486238704484550333450645980675647084723218680400038708259821002746875379967623768641382687888891957902585250332500270641073333102207539465376210181307720901791213924345119756758825834275372055980449266952616005825975555387716500817522824908432857026071665033012816778484145660697772438775947570824580751968890119224644480337206121139139960931936896495438490580120274219819634431878033441813045080124666648810444346334862324555615411291796867928283563787289130281557984780596508469449217893744004289280636206790654929475531109599188368464025877944166915314498404614649547497167549830589460416051460262090395134379178359996707303755192696440870466328095705320862210945665914733933403658892944393734878299458644702793404742656342135080525270197657975219761728197515530387960290508504522479278182948808410972213465135292594759976491136515662892639741176244499290347385487457494767993007406838789706336487154564074998865426473146293136275622451158641999031274598958248604351893254601585144826113667880558133984958635036080727223460168633341619010066802131392649256611975591608778355109397857200372013515532231462261731965273232780902680930635020848228821870261204002216214692997292332421049744320066469280275429216312520065573882596487927600013687698376136444495904212378522124062121848985118942554798207277600240214935257860347666512033640315354610010069311304779896037690388902546888562554658907264356107430142932702726193411178752431628619990029419988876079621804714765171360116374062530923602160805360048630192102748393753641119654726218199471357174254186859295130087652599379206307932853809898209795165190403954583336735058335198659519617220614747675824466754939891811874278047661699480465311036104208280825831509056774794461773972370245362981623456721757668573918886964641001946918218824298486598029959041150786584581657401307369508978116481313202140184932103816243889168153730855721150992183953062765777244598341017865259538963979670716112113081415386242559960175482826477535914181536659142152808343809501621553304623816058475693112225659506509883318046392746694624556788472339674515855988424407351416489877172373434476092412174578821415190214228194909622728302349995698936326721995
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Dense deformed trees
Mandel Machine, Mandelbrot Set

Very dense area with shape-stacking

Magnification:
2^1548.451
1.3495774588356448769953566853176 E466

Coordinates:
Re = -0.76521144337436612827618712788386264631431442320080875052533753601230178688355027726299806811170451611289200404299574516036180789026720371875088900237720267275460325661472230124314788353932516133715493371635574265207169279928193012019663808118151164078765931462641796338056559365257721246345636700553032129318498770389210482641436461892985688273722310754967770926769249242147119635772374166928893459597809212213848870365197441496541972493957854285889255117873589923615153400
Im = -0.09080159344980135046224266899038695656189142741028795997195219026419145543572388666654370295061216265859030738906358502546579272042627021497437056040111100659170594029903642901515609261693613501893683769152440374421577194717771846642896713757593234317730450197489346033811518180762128535808981059749751260884224042954158790728123849656153468368044819938956285460393330691938307492612269397197378591804884414268568742336255504680338999355029999117220194142414511268410102110
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Hyperbolic tiling with golden ratio tiling pistil
Mandel machine, Mandelbrot set

This is almost the same as my render called "Hyperbolic tiling". The difference is the center, which is the same tiling as in my render "Golden ratio tiling" except with lower rotational symmetry.  Because of that it looks like the center is fractal just like the boundary of the circle, which really isn't a perfect circle and doesn't have infinite details at the boundary. I'm using the word pistil because it makes sense if you think of the whole shape as a flower and it's a commonly used word to describe the visual effects of fireworks.

Magnification:
2^7617.253
1.0510843298882798169523444081002 E2293

Coordinates:
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For more than a year I didn't have any inspiration. Actually I think my last two submissions were even pretty boring. Now I have many new ideas again. I have at least 5 more renders planned right now, deeper and with more iterations than ever before.

I have so much to say related to my latest image submission "Trees revisited" that I decided to write a journal about it. I hope to clarify what I mean by the term evolution. Information about what it is is spread out over comment sections and deviation descriptions. Also there's been a breakthrough in computer-assisted zooming, which is what's helping me to zoom this deep.

This is "Trees Revisited":
Trees Revisited by DinkydauSet

Evolution zoom method


Maybe the title of "Trees Revisited" is misleading because it's not really about the trees. It's the same old trees again. Instead this is a variation of what I have come to call the evolution zoom method. In general, given some shape that lies somewhere in the Mandelbrot set, evolution can be described as:
1. double the shape
2. morph one of the two copies
3. repeat by treating the morphing of step 2 as the new shape

rare_glitch.png (1024×533)
In the left image, 2 points are labeled 1 and 2 respectively. Zooming in on the point labeled 1, which is outside of the "shape" yields the middle image, a doubling. Zooming in on the point labeled 2 yields the right image, a morphing.

Doubling a shape can be done by zooming to 3/4 (as a good rule of thumb - it's a little more complex than this) of the depth of a minibrot of choice outside of the shape. The exact result depends on the choice of the minibrot. A doubling leads to two copies of the same shape next to each other. That's step one. Morphing one of them involves choosing a minibrot INSIDE that shape, so we choose one, but that means it's not inside the second copy of the shape, so the second copy gets doubled, causing both the morphed shape and two copies of the original shape to be present in the result, which is a set of shapes. By iterating the steps, the original shape and every morphing tied to an iteration of the steps are present in the result and all visible at once. That allows one to see how the original shape evolved, iteration by iteration of the steps, into the final morphing. That's why I call the result an evolution set.

Here's what's new: So at each iteration of the steps we have a morphing and two copies of the previous stage. The way I used to do step 1 in pretty much every previous render where I mentioned the word "evolution" was to morph one of those two copies, but I realized many other ways could be used to double. The only requirement is that the chosen minibrot is outside of the shape to be doubled. I tried a few things and this is the most interesting one I was able to find, at least thus far.

Automated zooming


There is also a lot to be said about the computer assisted zooming I have used to get to this shape. Claude on fractalforums.com found an algorithm to determine the location and depth of the nearest minibrot inside a bounded region, involving the Newton-Raphson method. Because doubling and morphing shapes is equivalent to choosing a minibrot and zooming to 3/4 of the depth, knowing where the minibrot is and how deep it is allows one to find the coordinate and the depth of the morphing immediately. The coordinate is the same. The depth (the exponent in the magnification factor required for the minibrot to fill the screen) needs to be multiplied by 3/4. All you need to do is do a few zooms manually to make sure the algorithm searches for the correct minibrot and the computer can do the rest. Kalles Fraktaler has this algorithm implemented and I've been using it a lot. Some links to information about how it works can be found here:
www.fractalforums.com/kalles-f…

This is revolutionary. I think we can call it the best invention since the perturbation and series approximation thing. Zooming manually takes A LOT of time. I have spent days to several weeks just zooming for one image. Once the desired path has been chosen, it's a very simple and boring process of zooming in on the center until the required depth is reached. Note that this is not what the algorithm does. It doesn't need to render any pixels or use any visual reference whatsoever. It's a solid mathematics-based method and it works if you give it an "accurate enough" guess of where the minibrot is. Note also that it doesn't help in choosing a location to zoom to. You really just tell it "zoom into this center" and it finds the minibrot inside it for you, saving a lot of work.

It's pretty fast generally, usually faster than manual zooming, especially in locations with few iterations. Based on my experience with the Newton-Raphson zooming in Kalles Fraktaler thus far, I think it's actually a lot slower than manual zooming for locations with a high iteration count. Usually that's still more than made up for. You can work, sleep, study and (most importantly, of course) explore other parts of the mandelbrot set while the computer works for you, 24/7. If you have a processor with many cores you can let it zoom to several locations at once. Effectively that makes it faster in almost every situation.

The evolution zoom method involves a number of iterations of a few steps and I have found that generally it holds that the more steps taken, the better the result. The way the result looks like converges to a limit as the number of steps goes to infinity. The Newton-Raphson zooming allows me to perform more such iterations without as much effort as before. I always want to push the limits of what's possible, so I will perform those extra iterations, meaning I will be zooming a lot deeper. It will lead to shapes that are even more refined with even more symmetries and patterns.

deviantID

DinkydauSet
Dinkydau Set
Artist | Hobbyist | Digital Art
Netherlands
My name is Dinkydau. I started using Apophysis somewhere in 2007. I discovered it on a forum. Someone on that forum had an Apophysis fractal in his signature. I asked him how he made that, and he said he did it with Apophysis. So I downloaded Apophysis and started working with it. In november 2008 I started to do animations and I joined deviantart.

At the moment I don't make flames anymore. In early 2012 I started to focus on exploring the mandelbrot set in the program Fractal eXtreme. I knew about the mandelbrot set before, but it's extremely computationally intensive to explore compared to flames, so I focused on fractal flames at first. Technology and algorithms have improved and I saved up money, so I bought a nice computer. Now I'm focused on finding and rendering mandelbrot locations.

Current Residence: Klaud
Favourite genre of music: classical, deep house, electro, dubstep
Favourite style of art: fractal flames
Operating System: Windows 7
Favourite cartoon character: Donald Duck
Personal Quote: The world seems complex, but that's just because we're part of it.
Interests

Comments


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:iconflyingmatthew:
FlyingMatthew Featured By Owner Mar 1, 2017  Hobbyist Digital Artist
Thanks for the watch 
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:iconjhantares:
jhantares Featured By Owner Jul 28, 2016
MenInASuitcase Blower fella (Party) fella's Gobbler (Party) 

Hope you like the cake. :) (Smile) 
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:icondinkydauset:
DinkydauSet Featured By Owner Aug 7, 2016  Hobbyist Digital Artist
thanks!
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:iconjhantares:
jhantares Featured By Owner Aug 8, 2016
:) (Smile) 
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:iconfractalmonster:
FractalMonster Featured By Owner Jul 27, 2016
:iconhappybirthdaysignplz: :iconbouquetplz: :iconcakeplz: :icondinkydauset: :iconcakeplz: :iconbouquetplz: :iconhappybirthdaysignplz:
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:icondinkydauset:
DinkydauSet Featured By Owner Aug 7, 2016  Hobbyist Digital Artist
thanks!
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:iconfractalmonster:
FractalMonster Featured By Owner Aug 8, 2016
No problem :)
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:iconmeztli72:
Meztli72 Featured By Owner Jul 27, 2016  Hobbyist Traditional Artist
Happy Birthday!!! :hug: :dance: Rainbow Striped Spinning Star :yayay: - NaNoEmo 24/30 + Plz a cow can dance better than u 
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:icondinkydauset:
DinkydauSet Featured By Owner Aug 7, 2016  Hobbyist Digital Artist
thanks!
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:iconmeztli72:
Meztli72 Featured By Owner Aug 10, 2016  Hobbyist Traditional Artist
You're welcome!!! :aww:
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