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About Digital Art / Hobbyist Dinkydau Set24/Male/Netherlands Group :iconmandelbrot-portraits: Mandelbrot-Portraits
 
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Newest Deviations

Elephant shape-layer alternating evolution by DinkydauSet Elephant shape-layer alternating evolution :icondinkydauset:DinkydauSet 11 6 Density near the cardoid 4 by DinkydauSet Density near the cardoid 4 :icondinkydauset:DinkydauSet 6 0 Special S edition by DinkydauSet Special S edition :icondinkydauset:DinkydauSet 9 5 Density near the cardoid 3 by DinkydauSet Density near the cardoid 3 :icondinkydauset:DinkydauSet 3 0 Special wood carving by DinkydauSet Special wood carving :icondinkydauset:DinkydauSet 11 2 Recursive sequence by DinkydauSet Recursive sequence :icondinkydauset:DinkydauSet 7 1 Elephant forks by DinkydauSet Elephant forks :icondinkydauset:DinkydauSet 15 6 Density near the cardoid 2 by DinkydauSet Density near the cardoid 2 :icondinkydauset:DinkydauSet 5 5 Many stars by DinkydauSet Many stars :icondinkydauset:DinkydauSet 7 2 Trees Revisited square version by DinkydauSet Trees Revisited square version :icondinkydauset:DinkydauSet 9 5 Self-similar Dragon by DinkydauSet Self-similar Dragon :icondinkydauset:DinkydauSet 13 4 Cross Complex by DinkydauSet Cross Complex :icondinkydauset:DinkydauSet 6 3 Lattice evolution by DinkydauSet Lattice evolution :icondinkydauset:DinkydauSet 15 6 3rd Order Evolution Of Tilings by DinkydauSet 3rd Order Evolution Of Tilings :icondinkydauset:DinkydauSet 12 13 Three layers of curly elephant morphings by DinkydauSet Three layers of curly elephant morphings :icondinkydauset:DinkydauSet 12 6 Elephant spiral tiling with central transformation by DinkydauSet Elephant spiral tiling with central transformation :icondinkydauset:DinkydauSet 12 7

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Elephant shape-layer alternating evolution
Mandel machine, Mandelbrot set

There are 2 layers of stacked shapes. I perform evolution with 2 shapes, but between the evolution steps I also morph one of the extremely high ratational symmetric occurrences of one of the types of stacked shapes. The overall shape reminds me of 3rd order evolution.

Magnification:
2^7993.931
2.5882979488266437158498027473844 E2406

Coordinates:
Re = -1.74977473351308433946554680858057926568158071962806160157214596371394660395954890733614783436198144061946589313969954340796254161880794454689337556285417463144013304464568756825580144831469508137399241841846853405652268495084037241678543155873830106912862758117173842102427645753320347956610749579695828611801888613085987692473731422845158485311471337800123346524751523900956411418820290960750198521987744677384553939777389923715814143242562544518646491321234563918638819880798261813853940176877415873353717414992781230719323281775363535116768421496725266926977305705311729666678366475288999610429835785081682595724947183975915073579988740881312032883006113437042941788380054626116898973267286346011468339112193785123596576551566883878599657138669813177273350646777890884695856473346081750117129215011752630687728434813929262021623722141701584349846969551000904275938388038819870378863091701597219496970886193305612411023875493662451219355614883548083677193402253188634839539218657029639911682362660812179387157775932148423907412679387142611136931116387546434776752998840067263254262784587996470708729070456036816788411701678432569166181905336680395758426355636001121857746543143724619906240096440480321311973040754007196772246062638424667000270437473292182229264999098816785937960123045939545759260151990545095443637517248848906547060875174085457102319888845198698037647076657209332089054317367431007266204562956153206299329886908253505870848638864505836417545826973799842310856514297534264690928799780042346761251160888738915585857048103165081035252451637816570921042553744219811956498087087498408933478821717508115410614982796957430608862049199565565357985849840521898706269800496122639762655047047711859453220916408231401226070721830179827523025011303842939062158834641940041541176768772915064517372082099896521511309008868935348296185090958874357345045237943680722214018063927812345669411546883355402982997417281037949854907017208819364604758218020977663450153689339840170005236720509178192706164612367564371246633313418427872918837081824599672721442606611444343880694015210483296926046978010267239407978799032151061761392974841062765592482996040347439312709937246813684009325313683731259139726995199777024095276798618092045109170435644634514051352490297779427306095463039433984112157746588628684105844313288296807414929052423181273496370561002939064205710121729819867447237518218909242404285522457867126335300
Im = 0.00000000000000000000000000003514649090446868627177216845119135660468001726201493113147038904035846451602900274750466566486238052159244841375004186569707989971361966833098676431246312500185630274037110476959288692665293725054499767122158939889227242358364854409698676869130118070159435589794982124647480023336611292929195346229168479755755838898773037513424848600241462754815451434431337808100152964715089852726923708493525940352251060076504147569047509091951693130034402257061276902828664974980158956075098003479736180212107043525119754656775505126762154069204396777577480909057623822760261375982986105564814529063617487791144422022856980919151835072072142917992282378741591447649256542222620348772435071238249264205391554933088758899596980391600486233136454514785073758023659074640175993975706483049631761391464995180589591976427077464467837690023746834101277720020263868055554476743959355445625773843683032347670130508035129552753985433532817508507332590682498545769032843339074414105018995956260184836145171561977867214061179313580565232412283511678337342910790506720169840041675413021365693320282527222506670455942393623322957536654148193310997233091807029766917534574564179664818102888404646588093721111052202757641758716122995006335770816173377926081450819982086498999656608945580927292718490819027747320178451531744795751216818803378120531300805071029084736280637993486854065572363386574515250675108353819464933408126456071401174316830411198405105735025592506994729085028676845994948474627996816658811321793580164753792092704122620700018474119705813489598264066328160972214005175834490747195563970946642527523412925851133241211689591889482007635918670929153170102962492672244919352767715311563097687500446227645529068548814160128152046605013674572849731642313527342153573187546414213842482113488767585094392634058759234229790809621595951579155649762271701733842140008991237221176557910581280480616357727739866006268081601776424912710736862412184951898739460299144995918647540713315420906009466846069202179487116471532494471333077022735423372703010612296688899936394046019372275717362157444544981601842138599749194495354963889725267046904494702844438096762518474818722809333479490064671671745811420207338372437770179416591286842086961397728122769050657435137190163579890448695026618732799369664634568537182489470494001543497184919927109654952804768327538574957421884570337986998380744901611876535078926713600
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Density near the cardoid 4
Mandel machine, Mandelbrot set

A dense area rendered in 9 tiles to achieve a resolution of 79200×59400. Still it's not perfectly smooth.

Magnification:
2^24.2
1.9392560947398473961355372594916 E7

Coordinates:
Re = 0.18764408324767
Im = 0.55256192550900
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Special S edition
Mandel machine, Mandelbrot set

This is an S-shaped version of Special wood carving.

Magnification:
2^8407.801
1.0006877275353188871992296517181 E2531

Coordinates:
Re = -0.765725716774826008103371152975500188321618530776137094626506213493010178285774298246488264930293983561529572983469767091300863882820920219610230498720743769583938456617225726303988984202596212684740233771913098314944133923546892798227462835731432053414424644109505699220920493010040373757746157107697612863813600590094730123112102592526180023031859632909857694432619035505265947970468078331403412033945679349230691996432434991196554473957634842322529355128677193968863880301120101049730924162479179274706992417301102434280667162914455195695928420575056943903384594780268244168991986834866342209688078975211985477640004497132317355247933395281976199801022031167474033480805733350419616970697433678663710224018646536482728972857966151151505751700730905615039463872626078303518332963174104185595561032692530079838412015961451467937774563480969507949226332759741070012501020849675380941825551466585663206637241400401898372702565799679163561525884932172956321755492258543246127482872352536812539021464918926226530719161937616821785081653737593458324793888992248521427392021846524540111795577340795314992527556497179132346021600218101581477039633085439752900442890281743542005114503213387978947255303631946544565524945061361564209974714048856312459764028584985627702943376100209571848537787737182509956882048191045354334103141405754047071198130685696444317218986997915368643453110639808239471232558844314832029479172687895860257968106056393619417909022523810368977444121579842330549938721526251767529041838716341371992759322038290650783842344144618149016821726234409498875035086870445208099626196580498721982143589537524598901983776842825089253759188401810989912509741824732859128333039562620303174330206207256309945674747181427076810279771707868359288974655116322604713061228239698681282350693010396462936912870287327357750937297354277332758727572298762261354617115245553559747590003939698166210453194544530415647985783498834325360460557679390142746627801338376183130604818444199152106439155320220452272710296490794729962292252696420122348135247184582063437051867467609779839760826467923964687743813759039052786102662144493001230448859561722534074986904978046996051638551517408226566277754679530572411112261910792186926711252166919625873164981803861323072019048689290890828104988137691240923609478810542449065657256230951025931986193873975682903974091340596874171122645374292936182631756618257018781399043801152476483089193148104994943881053000803815793147512283103208152094369865444957068821052306507084109645424474305728940233043255412795000
Im = -0.097938070569041423777303020486914423956373992096113135417987735448427058614238959133500534728929964996934452382269648429366605251143484468810316365542092630639526122417777714673380639257688310087327788025641077468087915714786263833280123353136840324937560743182806375157496224322883699543954746235026751791508285794213872396185483038433942924361300428781201633137563726942187534522801045501176114342476843991114198715329763951835644538180467358652517736908530528769475282677341626969393656097289131031800533477404686718004554615645610806803320435668375523979887295947839574291038297358688973073140140794692871292276336510071352602235345099003039540516128593796920004435233606219887332525682143087836419936849810865023409585684201155464838615464317310093626815817425432764575417831777402185404981051030067420288373139450110913128719024092969793048149540439701719443903794634517286098921171004592245746975751937165920165316450493454908060571762364512815931377786135109392191556695614536964442790338150688333882223877369630075984512222687074184659152424198784801752831534427349406721619029571371302633145360582180924668090086562954228712375396375100509910786628309523101105175217705094974915439470673188336313025382806324268307335656554528856715318032612296098157459635443913332215699452248109589431990182342154660855029087246855720708661896158950550369613651093560376116830508581764758131032798768908810314127538401531388161495181390045010688386806124972588927197954730641092280526896236690071359228492846964598342169218562201666217872016310898963616974771547845571081027260759959511732436804254998961626553435446557290184372801464139676796439325205537009046120221146447187837184918626170453031406112683399086192582450971234733609834593141005283886973598261730761259183996938804438274932949378003037449583509326687818656276084035972238242271518569596723722793761565170978904161639058647715873234264424529634682050711404989946378014571727295558888445223534382068457691938777622140465914875273800568950259982158810410583473317424146937065636871510892761874803609312829012988939189474944123129657615597028121670200211455097482212867376354263039427967893556888786365102093067618201100052853590895091900555210899872197422159525791528353496828193848452492611463094909341315449613013557973943868673364373445821470174685653608768493875019150147603181407552756414756071763460534675702949231459363608777690671200859964051018370731454818697305910692081086826694067498531432273545805700583742580577239096066783756298549556789013965866210127846970222000
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Density near the cardoid 3
Mandel Machine, Mandelbrot set

Again a location that's not deep but super dense.

Magnification:
2^35.769
5.8552024369543422761426995117521 E10

Coordinates:
Re = 0.360999615968828800
Im = -0.121129382033034400
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Special wood carving
Mandel Machine, Mandelbrot set

An intricate pattern of connected spirals built out of an elephant valley Julia set, combined with stacked shapes for a patchwork-like appearance. Around 175 000 000 iterations were required per pixel.

Magnification:
2^8347.59
7.4986227425376759404742408881183 E2512

Coordinates:
Re = -0.7657257167748260081033711529755001883216185307761370946265062134930101782857742982464882649302939835615295729834697670913008638828209202196102304987207437695839384566172257263039889842025962126847402337719130983149441339235466910083497396626923010217735238914270163009695695287930817753874112097270497104593741980771017589230549209718812130086470817948225740335882119856914908896649129776322678316151022572502808069311729691076551605840077742574129197098735274761983332532015056895199636164868058633722023206514842775322610879155991812930258736636213294049915066280715268039631394103955185068708954064715923215594978858986110771918238247814312977250996766274855429342385045715610194340133177886744484314886707313723399304691755582477103314987189577455513344506479347997697039719242001322605470410509325925777523503113715622126837007912927635871100115574505162443403527624048159551323019601657259326898900338440834516024872441189310085655496132848907959488973503872467451884229573753240652445340372260582314468633233451699984740669855631490920415384052420684311576780326757290828249453457229743871142259490289726339457754323890776454148804134365546654368290234358442427377798393562491399119422797982565848152147366127992659283832184167201730539365355164329861452920364184559953642376366149850996850805152236728240233679997046335613743857415845068802992164832306966180925915806151850654054010220156661582468095698106333898504922792219634688809893791420330810707687234011018897221169989570303556483466330589385461600261175428062618485240534880178479753573999424933520199719142085668764288646103633238629858421942750566188515991757880484538576286047440263390051134449305748236353168907065878869437386826537031617521861646065715442326899009618784010258346213991145087334492942696641108710828663937686753680747236453636524370757998312020251704419505550417847964177831163936810783818288712758598342768542900062162146350662318214069464310703388050885261733435474789837141971480676459215461224774715315327818060063136264001007235017265482761907402268037830781015655454568118884783057586787725999916667920207288966594488140590348450389562235305254940176410903807352813095397840634606662475722327333681562685194317990786745728085730108156342844709552032358544919181299232467595597092521780972156002416275979169291365100161235929761009942299944704810030537312412880158289196944218750566420041566743520852651674891163923430975362280283296972471457476860820441208582034794846441902719106631658019911773980082707532450643613041307288
Im = -0.0979380705690414237773030204869144239563739920961131354179877354484270586142389591335005347289299649969344523822696484293666052511434844688103163655420926306395261224177777146733806392576883100873277880256410774680879157147858127810789568835921889235175168212003501996315657749279155461876008333911292404563062073768806065629153869941025041865181964585005594541922415545130308039955608572661853273398570046707839888649455573949475777370929770943589100178258631152673723305757247296329700955195675224898105836761437438790085283372413657355422433601429459340930673387253768911620999713028549482516816171501921191785137315373546791944160033516258495851492637274084158284267195512404874518255519585070567371925200334206162537066025863950278374506831306348582709401223093777343630356917989944133417478247555201283865792854673246896306413060288713905201446068899500805748275513480218453585160593044324052626535141595297683179823823475061354325703863936777980183811131040508438887255748023809825960522237546754319055646415271948618417756325371724961477494588208707873206075817241526130404477572294828306747288851193543871054773423865013687775441959059024627078216826740980280262542746171652006007240734942744824524723025579925602150241186152360593497706338657793821278232608575302912680371509844789792390134458242698325647144273149823161701576775114663749343709034070342846336789263928957374486439583649182590813760496593755459786412516082227994891439983103514459075766512146952591229056137038305411005937511114118653561377917019024822063525108863610536622266328479961475205843459624760503663015250882451091524204160400844829839100233764453804428330755532968950375271357895901183319619665697261458973864911680570477237395481126799363871468299051676686737058936057693901021234952257174010554311241835642257550087117821853825010097652604802161536620149802046671733944548644518355164637882036817618311343568134924360107095362415405247212783010801384241851578599191377214008449362097073451629355052293395706815211898069671261098425238328356914339341168006300971244410666472110112805481252869603953791806688943402606744422877952042707827783383526255307298670626706119466853903208321688901000533309485153171856178296015210127832107798808565898397663936167253413224572412258077115226903767644102112085257466681088339460415558157030571983514915467243605791153999145436838230704835755727726136753701444065321353606599306142833428361336143402700273323452520474426060161141379885127892542602995926883756785703005601927227980397787759795
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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

julia_morphing.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.
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:icon2born02b:
2BORN02B Featured By Owner May 21, 2018  Hobbyist Digital Artist
1000 thanks for the faves and watch, Dinkydau. Take care!!
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:icongs13:
gs13 Featured By Owner Apr 20, 2018
Hello,
Take a look and tell me if you want I delet it:
Gs13_Deviantart_058 by gs13
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:icondinkydauset:
DinkydauSet Featured By Owner Apr 20, 2018  Hobbyist Digital Artist
Not a problem, because you mentioned it's a reproduction and linked to the original.
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:iconfractalmonster:
FractalMonster Featured By Owner Feb 3, 2018
.. and also for the :+fav: of Rug Hiding among the Seahorses4 by FractalMonster   :wave:
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:iconfractalmonster:
FractalMonster Featured By Owner Jan 4, 2018
:wave:
Thank you for the :+fav: of Bridges Building the World by FractalMonster   :)
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:iconadapterr:
ADAPTERR Featured By Owner Nov 5, 2017
I had problems with my e-mail address in the past and I had to delete all pictures. That's why I'll upload all my pictures again in the next few days                     

thank you for reading:) (Smile)  
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:icondinkydauset:
DinkydauSet Featured By Owner Nov 5, 2017  Hobbyist Digital Artist
Okay. I was afraid you left the site.
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:iconfractalmonster:
FractalMonster Featured By Owner Oct 21, 2017
:wave:
Thank you for the :+fav: s :)
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:iconkarbock:
karbock Featured By Owner Oct 14, 2017  Hobbyist General Artist
Dank je wel voor de :+devwatch:, Dinkydau! :)
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:icongblxviii:
GBLXVIII Featured By Owner Oct 8, 2017
Thanks for the star!!!:D (Big Grin) 
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