Title: Dragon Tree with Crosses Post by: Dinkydau on May 04, 2017, 02:49:07 AM (http://pre07.deviantart.net/3873/th/pre/f/2017/123/d/3/dragon_tree_with_crosses_by_dinkydauset-db8115e.png) (http://dinkydauset.deviantart.com/art/Dragon-Tree-with-Crosses-678613010)
Mandel Machine, Mandelbrot set This is very much like a normal tree except it has a "connected" interior with some crosses inside it. The crosses are achieved by making a stripe out of a low-depth embedded julia set by zooming into one of the main spikes of it, before doing anything else whatsoever. Then, if you deviate from the current zoom path (=the way to the closest minibrot? I think that's how it works), the first things you will see are the julia set and the stripe again because of the rule: If you deviate from the current zoom path, you will see everything you've seen thus far again. This causes the stripe to be all over the julia set. Each time I increased the number of arms of the tree by morphing it, I zoomed into a strip inside it, thereby morphing the stripe into a cross. After n morphings, the number of crosses has reached 2^n - 1. This technique is an exploitation of the fact that "what happened thus far" is just 1 thing if only one morphing has been performed. Shapes other than crosses are possible but with the severe restriction that they require only 2 julia morphings to be made. I wanted to publish a new render sooner but I couldn't due to computer and internet problems. Magnification: 9937.724 3.5728322825644750137997369306096 E2991 Coordinates: Code: Re = -1.674364274409247056603320660316824291970062080466541705865560857514382711264381692391451883778167828857329201573088543356588985766062306089895493333839285042788226726677595275366306242750145216885463147565567474862604416261650846284872472465600450893875524615783023617525710353201753108424509867471987138259001030929193190257819073677175100723852940699115248913293168821487104061449545491631051406293054976737459367481850008115092269818719734865312103974302210015932153840455404040157021485400702101168210188771065769722284590129215517165387174500770793312078593263338312594734548134878619509663429586307547732042821766089499919742900707219606915115849846801107087520881411133151676030353408340982573470025825761630441460328129901466249305886338781941212603012374275159494065916072249954878131716732287280011025965861954279370136215182084540844059744932438037348130437853167311846775225704650375858138851127822075084116361941938914845130880136934326125923195131408387017248499188412482964345903899167305387562133010549689893116398282067318135507950676416282694063841483392803688797051776281618715564589820037717309455570188774581997239588388350010896731676949877670747009414625621358296846538667790799726441198100364300343046328393666959818708022982397960166464337974286727140690404934174725525367050768641098770911362560825038751962502526899632804940268295378718753613181256415892883387487578373020210726434716909533954219074351036105687479708986970938006524819499490191710248908640269568407347625381390710334138559123133945780970959415656043832501672797883930756333910229726824291965947826807054218203617943739661160966129744228079904915302657670156019053530875304491508694706669262099444154674173996825443294545330740312620297851767049976911599032063855417151818935495914521815410009393008276881759426938274326547667749262733114170356888447566163396116220555016322626579988097414618977911188245538396896242976964208367430484740914354354528808307152787999057668887103517988627124267089471758240320611809387082004487035345009122755385997984145162488913787106975210603811467950410491633850332653831663071408005434622635171169985863573277688673027292642172734040779969307366509521300841222857437913686314792646647028800345640911788424421367051102200944116602994432427570544317350529438499599780444345183597397644823580098767289539464663268209626604647709544185679901285362670310529049634322640031020909033611307225896851076488091273514348023315970064480536354408463272202124192636623090058926964005367999418811975933355629375354240368054332341818538310934418703362565445715152002093582223578198857156572708021877000145696658169354591325063201633608232156674959072843115622394357111645826411812810925045168630404874260497850744961467429362371018169829441663779912873383465377392315629330724767906707072002408246102902518571639116851530501918164958403283652496104465910387686114717039643792567655290370494523755672818407386924171118632398933629073020312842337862256353043936666033255729927952494209336 Title: Re: Dragon Tree with Crosses Post by: Kalles Fraktaler on May 04, 2017, 10:52:38 AM Nice!
Found with Newton-Raphson I assume, using Claude's KF-version? :) Title: Re: Dragon Tree with Crosses Post by: Sabine on May 04, 2017, 12:02:32 PM Lovely place you found there! O0
Title: Re: Dragon Tree with Crosses Post by: Dinkydau on May 04, 2017, 12:38:10 PM Thanks Nice! YesFound with Newton-Raphson I assume, using Claude's KF-version? :) |