HOME | DD

Description
Mandelbrot set
Computed with Kalles Fraktaler
Colored with Mandel Machine

Sequences of things in the Mandelbrot set can be morphed by zooming into the things one by one, iterating through the sequence. For the image Spiral iteration Julia ghost I did it with an arm of a spiral. That's an infinite sequence, but it can also be done with finite sequences like a ring around a minibrot. I did that with a ring around a stripe, as they can be found near the spike of a minibrot.

The overall shape looks like a Julia set. It's a consequence of the how the zoom method works. It made me wonder whether all Julia sets can be made by choosing locations for Julia morphings manually in the Mandelbrot set. You can't find a Julia morphing everywhere you zoom: there are iteration bands where you won't find any more detail. The only way to morph a Julia set is if there is some pattern in the right location. Theoretically, you can zoom deep and close to the cardioid until there is enough detail for any desired precision. That's not at all practical. It's not needed if the location of the pattern used to zoom in on somehow automatically converges to the right location. Tests so far indicate that doesn't seem to happen. And I don't know if there are interesting applications possible. The shape of the Julia set to be made determines what kind of shapes are inside and they may not be beautiful. But the implications of it being possible are pretty crazy: you can build your own complete Julia set with Julia morphings and use it to build shapes like trees and tilings again. I wonder what that looks like. It may be too deep to ever see. (It feels like hard to explain again. I wouldn't blame you if you didn't understand this paragraph.)

Magnification:
2^18520
1.23787960218E5575

Re = -0.14798211722916711785116195827066107853304341920134511919124562570713516500357695901524354557997603206762618350518450967914500007638333899679743199558652554031594382900188738300512660620024902520740756242436753747764353450185237496944700431605516868096200620257383342357209460820022468661915584969427069644472763124997021515177342002428991065900701481593945173062533524412662550169625977928133962802920701104958210993925582441469591708374070616829201191553827257566448886891940241780018837535102442780972891031017133655132902077436100616938260150592843298114543540591621791647795440045707713988416141103924107835617727254415480598764787279102001166600407676681140789296846558473301931044447361765969897833882968409501085826454148134012856717076729145469665416531405405941349868449476358378628228326393325366156919888197500467820956032050334178882580946685209212016024441207050037641485659840421520061489288834993145983236285859034891912244810665112525185005949623576691151030649458320686859854323498630110715453410803184160133211626736131038842290525539950358046130945846132222363669671554679249718851083127659666221794340841093124017307680582966566180956164438389411297092439134466041047845596154757006477415285928308799277074092978945877110069953797103163642613856970055877582486318845712109710960838097927495622443819476525900072506230125551041805840829971267287078703686519213767900907548940063406881557364184114969624325138070025893105169624580625466151787503437833221659802546659584785539116033799486687749460233947346560320676625795832353535286379447489897809578532679381448465945564370615633073268445756435906334625020753432231467298304685438676233118969308959062166996192032656851162349545793314109619297109315689173265270803825394996384874958298984515714499883494061109065039381990725890822440580642969439291380635347208640895414062247177701447893638015611221904605036804062884470417557284050601019169358672403895641350212825901327771690517703956500146388198148416817191806746728827091739292486224107262053709636321676721088121388061536229761697704212726231780408932084893249780106628063196581767220818071645406604508564679326806215696452784601589479440632976775669916726997869251764643275794826703046258262033767458341768226945265055306886906610780825470223438464356667623015568761928846681162220833279815042493044375546309100241609811540720250312213380783267184913577367609158064223023869313930160306417620587271815803296283195014065369174426261367692890357451188893928372605573778757631690295714193235585020534653723838104730116333692391587331067492686320742158159959512279335512678199287370514919055624015363897088541160754272627242659616265768187482831969618975865842565881003883256876221918381956035733740672332306070014019488244915405731040967805483129054837639695653876815064040304521224718294023425795780743664163156079128331393280726099953762447568939563548598747160046186165675785891151388090037391649563980552360277893134467110738674315585269458477244042437187679537223453522988822881074738722183663161206754155018172496837834296647596823237625398786402372593289886141856068860834134426501254309453985654278150192069057586492569692962333689120353490054751039493014867473564345257351646527005217575319821312790671711751339145993812700744294494186951324091893899782683184028367736242354091711420719951213315191512628144859108476127528694175275394323577970877964288521915930546807905320693784333006522364087342201835821410246164630140341483227741827862668556767784961886149025791268893891689785505954908316315290670828061883135765049463101629861510358232572292121818829583454689225566366988530302393745958178394970144197356457300824842806789397655677860608953923672753302278082317635193023117643917801814182912960751395363411038405952646050855063040089926783930694878346198885509272693788588498775506371780959374077140175640546983004165570983472909995506459036437281557605861174076434024254904909232386630768378703002207301831481514195312724340530759282674964849923364564690927273224583693891601259927812233108403931099354939465749954794104919841383466458301458790658856156518625100761219084977613982963020360487983773240638235472450985830188952099197283916938352827087485688047444033966411958966083310265589268470244292931820891226726787812132274444652957759479127445778328694620731674361975119892847227743863477923009670952243564356042089188321964554510172269723247506596231980189552585278008332550057879159148045769438824024777363612155037554779500196905028578540656252394218355284087051464486563796546724079398766884623384281380397219433519438154850664326516469016270273210008702755467881261926085606031599948746065116975953815239441096730768116748912457170806048968141346053606975943797865127042211822089290735108265510771271522600800504266395942691562153853471745882371430437200787400834965552851918178147873742160191101994176738386885556477524029019788853348081398324678295466190289063654097788621564956460894462855715038960960930655301974198938128228684938287441517722473830568416866518884562078511420684727410125047727998145070676862313399561826556011527854531282651648209599014905871502835770450431282150755229694330289184907397050609715749443073166850271593532075934949890623217229172718306171735768616513550745630456179115321757126310536375522836395372814697215703904823462491723717461827473618841001248236520423334785159063501248898795637678533683927983599516138660239744874810618262315901488687645018366331913066024161511489460854210923694286773882459770842947331901695270962016385125135545388352606632691975896703057870067050940979178129650259213014471655925143724609000002

Im = 0.65151160881599962882378298092714682263739698626343127053897842148581696146823375196270347180103890435676122398079423201588918060643819843335016817536816949407142117060615008159663670284652610521987317339141895152151119565411721479676274551570228331674722052104861525996045290130077503240534240590205187212934541813361689509924542610649289271591206689669989455042140058873447756635319054311453720107050111252593475357243351029084164947275103090180463158550595059422480723255332677768194954954606896630423161070638504993759075081004972848729625804962613418071239141903489822156933175810219353012528737423071464225824440682765763237157171445520447520978598994497295443905343411174224233387513313628288033320982491646295671090205931221062455255340110759731035096876934584201964441224294249764979736007828855417827272691470149330758920546674443555235703134369663862608183897320675990563408324571048786185941121027411688933888529457504852251784819382079312018361216357254132294742694408348253909595409541654840710317940104421904517234352690045846521459501211095028109214282386522751697777124461090995990644171306463676032980722347043999336268876962814142595011795537760985093605812408282656823774870325993028816945838952635441857956230159637022657417474750132183612091731580010980736814757295213626278694024614701090907342584046316113557617455546606848898996594778304941199005723319394996478159788304404120102310052949949027496090212105006697183119576088204190728583350376475259247148165932349587350632043753268860529183723090680607238345842579373919205504870909003485988853080227677744204814089410819627865522458460730074234855812193876250733876521278141750120061358424095350552266801313392047386965686154329173861347587746163443391986013733526655144993045301040986424310878564416331376773708168377819063046587726778645004398380942496495209364385649630163386436609989936890113320543394584581201840561386113511207773844239958160318809971109251038866265113175340365635725303441685132987235560497143480875321993290966450812142904936904011253905653789836192387963376864410129139029595266274938931553443624770119491942316596148273635054154994889799916341218795767337276121180787761259141554246855180826812658008618690852686412529972011404970466997261613791167410618806008106137212495810142896014683690422497938968560254795954127615373455784690820509768505910007949645300914571608397913220474054371732954711301002032557966825198751478986329955563540470043327416852491659130260548950207776846758270849369447591698288155982168415171735850403321966902585412912571135794410637615784627915767414661093226355664791095159082039087756883911192499641082161065958644622743564399539339074536792493921335014107739620078355264491019886272613355560508670211623045698325554184026709814067809527793367332758854867561493326442110657800913795868882301136615212859079445723571442183555183503755965114195054222948265733137947486297957015638632727405882210611845210670164160888330303262440289229276385832736961243059515016817014320295963446784364994517551333633115836420511058569401070696427936199476642130631666629937905676063289172611242854080816124928216856535807009632684562083243285441367670390300520612858140179089948662880094454008557356492177880866094853731907936311104444637132864132096606704197052311876092817937986530548701798459657203788117673648890578435433508961052937924356933903712115412943699981693112428740317549008212303552929185228309830792672420537604788731587535440055284008146681311023775683205535324966184624090844086156572210374465011254490454372334048035410408072195994781073393383216744749946956898933618978749869988522939742243196225916942470450301245836750309799656881365826355010834424147910171158543053389588722658488542209341867217248546800515615295396213377504113660748924904316311913886825402732066148685525788127395407231290506106281946194220131926387929666272542925595279309593291170119404015308219093757821296590527751939735648668503519400091618872930161037868929619366357112406163239967119720309535962194027418440629305402399033963090093077647632126039534183450751209679104036072162686425979635754005781209119942834172200505602506654047802573288120800880375207592171134418234501254510116127942478895657720921706341170032816735722581728023596074579071360552857358046492690429392055913493914347951370661216116564501961880274092444146727012772990691703563932094955660444808019823394326117236930661750440240415987333613821187362474016488389157347690221972000695031530452937129447849563042730120555271057110624777237672176618516123240202968390019261069184288213469438879276044430652229748523759787477168007391653974970694400095007935783235034396696297449197880553845252373650728259296760149546680379547593874314940714024155353701117966129539598196167271261922845745835539378633551802735057991818351106123406091630424964078037834708715949980302599080707029655661916977477782076206850594528154972322675531856971182082649928606244364852164277629555087683864503405924793417289835611953805075681201073565339737012176948843353574686347486991644832565927281071454566027898067902964539336350950641006523453747551318825095887093195892314946162536670380383232830402145747900626131616680066622658644670601926055194090307639743408677142792222593292551145188142289795324713261594556046331793860670503150571482599877144746898331460413698628263342671797425848281939466110983022023377899450347197787559995910717337581023940080155999508080220445593461850502008667982131022749750307408011912603039782122583065901772364522178390709720346786895798814295814498446824057033101753276144562528534662505570858070718476582374999966

Description
Mandelbrot set
Computed with Kalles Fraktaler
Colored with Mandel Machine

Sequences of things in the Mandelbrot set can be morphed by zooming into the things one by one, iterating through the sequence. For the image Spiral iteration Julia ghost I did it with an arm of a spiral. That's an infinite sequence, but it can also be done with finite sequences like a ring around a minibrot. I did that with a ring around a stripe, as they can be found near the spike of a minibrot.

The overall shape looks like a Julia set. It's a consequence of the how the zoom method works. It made me wonder whether all Julia sets can be made by choosing locations for Julia morphings manually in the Mandelbrot set. You can't find a Julia morphing everywhere you zoom: there are iteration bands where you won't find any more detail. The only way to morph a Julia set is if there is some pattern in the right location. Theoretically, you can zoom deep and close to the cardioid until there is enough detail for any desired precision. That's not at all practical. It's not needed if the location of the pattern used to zoom in on somehow automatically converges to the right location. Tests so far indicate that doesn't seem to happen. And I don't know if there are interesting applications possible. The shape of the Julia set to be made determines what kind of shapes are inside and they may not be beautiful. But the implications of it being possible are pretty crazy: you can build your own complete Julia set with Julia morphings and use it to build shapes like trees and tilings again. I wonder what that looks like. It may be too deep to ever see. (It feels like hard to explain again. I wouldn't blame you if you didn't understand this paragraph.)

Magnification:
2^18520
1.23787960218E5575

Re = -0.14798211722916711785116195827066107853304341920134511919124562570713516500357695901524354557997603206762618350518450967914500007638333899679743199558652554031594382900188738300512660620024902520740756242436753747764353450185237496944700431605516868096200620257383342357209460820022468661915584969427069644472763124997021515177342002428991065900701481593945173062533524412662550169625977928133962802920701104958210993925582441469591708374070616829201191553827257566448886891940241780018837535102442780972891031017133655132902077436100616938260150592843298114543540591621791647795440045707713988416141103924107835617727254415480598764787279102001166600407676681140789296846558473301931044447361765969897833882968409501085826454148134012856717076729145469665416531405405941349868449476358378628228326393325366156919888197500467820956032050334178882580946685209212016024441207050037641485659840421520061489288834993145983236285859034891912244810665112525185005949623576691151030649458320686859854323498630110715453410803184160133211626736131038842290525539950358046130945846132222363669671554679249718851083127659666221794340841093124017307680582966566180956164438389411297092439134466041047845596154757006477415285928308799277074092978945877110069953797103163642613856970055877582486318845712109710960838097927495622443819476525900072506230125551041805840829971267287078703686519213767900907548940063406881557364184114969624325138070025893105169624580625466151787503437833221659802546659584785539116033799486687749460233947346560320676625795832353535286379447489897809578532679381448465945564370615633073268445756435906334625020753432231467298304685438676233118969308959062166996192032656851162349545793314109619297109315689173265270803825394996384874958298984515714499883494061109065039381990725890822440580642969439291380635347208640895414062247177701447893638015611221904605036804062884470417557284050601019169358672403895641350212825901327771690517703956500146388198148416817191806746728827091739292486224107262053709636321676721088121388061536229761697704212726231780408932084893249780106628063196581767220818071645406604508564679326806215696452784601589479440632976775669916726997869251764643275794826703046258262033767458341768226945265055306886906610780825470223438464356667623015568761928846681162220833279815042493044375546309100241609811540720250312213380783267184913577367609158064223023869313930160306417620587271815803296283195014065369174426261367692890357451188893928372605573778757631690295714193235585020534653723838104730116333692391587331067492686320742158159959512279335512678199287370514919055624015363897088541160754272627242659616265768187482831969618975865842565881003883256876221918381956035733740672332306070014019488244915405731040967805483129054837639695653876815064040304521224718294023425795780743664163156079128331393280726099953762447568939563548598747160046186165675785891151388090037391649563980552360277893134467110738674315585269458477244042437187679537223453522988822881074738722183663161206754155018172496837834296647596823237625398786402372593289886141856068860834134426501254309453985654278150192069057586492569692962333689120353490054751039493014867473564345257351646527005217575319821312790671711751339145993812700744294494186951324091893899782683184028367736242354091711420719951213315191512628144859108476127528694175275394323577970877964288521915930546807905320693784333006522364087342201835821410246164630140341483227741827862668556767784961886149025791268893891689785505954908316315290670828061883135765049463101629861510358232572292121818829583454689225566366988530302393745958178394970144197356457300824842806789397655677860608953923672753302278082317635193023117643917801814182912960751395363411038405952646050855063040089926783930694878346198885509272693788588498775506371780959374077140175640546983004165570983472909995506459036437281557605861174076434024254904909232386630768378703002207301831481514195312724340530759282674964849923364564690927273224583693891601259927812233108403931099354939465749954794104919841383466458301458790658856156518625100761219084977613982963020360487983773240638235472450985830188952099197283916938352827087485688047444033966411958966083310265589268470244292931820891226726787812132274444652957759479127445778328694620731674361975119892847227743863477923009670952243564356042089188321964554510172269723247506596231980189552585278008332550057879159148045769438824024777363612155037554779500196905028578540656252394218355284087051464486563796546724079398766884623384281380397219433519438154850664326516469016270273210008702755467881261926085606031599948746065116975953815239441096730768116748912457170806048968141346053606975943797865127042211822089290735108265510771271522600800504266395942691562153853471745882371430437200787400834965552851918178147873742160191101994176738386885556477524029019788853348081398324678295466190289063654097788621564956460894462855715038960960930655301974198938128228684938287441517722473830568416866518884562078511420684727410125047727998145070676862313399561826556011527854531282651648209599014905871502835770450431282150755229694330289184907397050609715749443073166850271593532075934949890623217229172718306171735768616513550745630456179115321757126310536375522836395372814697215703904823462491723717461827473618841001248236520423334785159063501248898795637678533683927983599516138660239744874810618262315901488687645018366331913066024161511489460854210923694286773882459770842947331901695270962016385125135545388352606632691975896703057870067050940979178129650259213014471655925143724609000002

Im = 0.65151160881599962882378298092714682263739698626343127053897842148581696146823375196270347180103890435676122398079423201588918060643819843335016817536816949407142117060615008159663670284652610521987317339141895152151119565411721479676274551570228331674722052104861525996045290130077503240534240590205187212934541813361689509924542610649289271591206689669989455042140058873447756635319054311453720107050111252593475357243351029084164947275103090180463158550595059422480723255332677768194954954606896630423161070638504993759075081004972848729625804962613418071239141903489822156933175810219353012528737423071464225824440682765763237157171445520447520978598994497295443905343411174224233387513313628288033320982491646295671090205931221062455255340110759731035096876934584201964441224294249764979736007828855417827272691470149330758920546674443555235703134369663862608183897320675990563408324571048786185941121027411688933888529457504852251784819382079312018361216357254132294742694408348253909595409541654840710317940104421904517234352690045846521459501211095028109214282386522751697777124461090995990644171306463676032980722347043999336268876962814142595011795537760985093605812408282656823774870325993028816945838952635441857956230159637022657417474750132183612091731580010980736814757295213626278694024614701090907342584046316113557617455546606848898996594778304941199005723319394996478159788304404120102310052949949027496090212105006697183119576088204190728583350376475259247148165932349587350632043753268860529183723090680607238345842579373919205504870909003485988853080227677744204814089410819627865522458460730074234855812193876250733876521278141750120061358424095350552266801313392047386965686154329173861347587746163443391986013733526655144993045301040986424310878564416331376773708168377819063046587726778645004398380942496495209364385649630163386436609989936890113320543394584581201840561386113511207773844239958160318809971109251038866265113175340365635725303441685132987235560497143480875321993290966450812142904936904011253905653789836192387963376864410129139029595266274938931553443624770119491942316596148273635054154994889799916341218795767337276121180787761259141554246855180826812658008618690852686412529972011404970466997261613791167410618806008106137212495810142896014683690422497938968560254795954127615373455784690820509768505910007949645300914571608397913220474054371732954711301002032557966825198751478986329955563540470043327416852491659130260548950207776846758270849369447591698288155982168415171735850403321966902585412912571135794410637615784627915767414661093226355664791095159082039087756883911192499641082161065958644622743564399539339074536792493921335014107739620078355264491019886272613355560508670211623045698325554184026709814067809527793367332758854867561493326442110657800913795868882301136615212859079445723571442183555183503755965114195054222948265733137947486297957015638632727405882210611845210670164160888330303262440289229276385832736961243059515016817014320295963446784364994517551333633115836420511058569401070696427936199476642130631666629937905676063289172611242854080816124928216856535807009632684562083243285441367670390300520612858140179089948662880094454008557356492177880866094853731907936311104444637132864132096606704197052311876092817937986530548701798459657203788117673648890578435433508961052937924356933903712115412943699981693112428740317549008212303552929185228309830792672420537604788731587535440055284008146681311023775683205535324966184624090844086156572210374465011254490454372334048035410408072195994781073393383216744749946956898933618978749869988522939742243196225916942470450301245836750309799656881365826355010834424147910171158543053389588722658488542209341867217248546800515615295396213377504113660748924904316311913886825402732066148685525788127395407231290506106281946194220131926387929666272542925595279309593291170119404015308219093757821296590527751939735648668503519400091618872930161037868929619366357112406163239967119720309535962194027418440629305402399033963090093077647632126039534183450751209679104036072162686425979635754005781209119942834172200505602506654047802573288120800880375207592171134418234501254510116127942478895657720921706341170032816735722581728023596074579071360552857358046492690429392055913493914347951370661216116564501961880274092444146727012772990691703563932094955660444808019823394326117236930661750440240415987333613821187362474016488389157347690221972000695031530452937129447849563042730120555271057110624777237672176618516123240202968390019261069184288213469438879276044430652229748523759787477168007391653974970694400095007935783235034396696297449197880553845252373650728259296760149546680379547593874314940714024155353701117966129539598196167271261922845745835539378633551802735057991818351106123406091630424964078037834708715949980302599080707029655661916977477782076206850594528154972322675531856971182082649928606244364852164277629555087683864503405924793417289835611953805075681201073565339737012176948843353574686347486991644832565927281071454566027898067902964539336350950641006523453747551318825095887093195892314946162536670380383232830402145747900626131616680066622658644670601926055194090307639743408677142792222593292551145188142289795324713261594556046331793860670503150571482599877144746898331460413698628263342671797425848281939466110983022023377899450347197787559995910717337581023940080155999508080220445593461850502008667982131022749750307408011912603039782122583065901772364522178390709720346786895798814295814498446824057033101753276144562528534662505570858070718476582374999966