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3rd Order Evolution
By DinkydauSet   |   Watch
9 7 557 (1 Today)
Published: December 25, 2014
Mandel machine, mandelbrot set, z = z^2 + c

What to do when something is possible for any natural number? Just call it "order". In May I said that I had found a way to extend the "evolution" zoom method to work with any natural number of shapes. Thus far I have never made anything containing more than 2 different shapes. This render shows the effect of doing evolution with 3 shapes. There are normal trees, the layered thing that appears in the center and long stretched objects, all visible at once. The reason why I hadn't done this before is that the depths at which such "higher order evolution julia sets" lie are ridiculous. At a magnification of 2862 zooms, this is the most simple 3rd order evolution julia set that I could come up with and it is made with just a few iterations per shape.

This render gives just enough information for a new conjecture. Recall the conjecture about 2nd order evolution sets that I mentioned here:
Prototype of evolution
"When the method to create this structure is iterated infinitely, the overall shape approaches the shape of a julia set."

New hypothesis: When the method to create an nth order evolution set is iterated infinitely, the overall shape approaches the shape of a julia set of the type found in the (n-1)th seahorse valley. See:
i.imgur.com/rMea5CI.png
2018 edit: This is FALSE. I don't know what I was thinking at the time. evolution of evolution looks like the second seahorse valley and evolution of evolution of ... of evolution (n times) looks like the nth seahorse valley. I verified this for n up to 5.


Magnification:
2^ 2862.649
5.5362546428023729586009972615094 E861

Coordinates:
Re = -1.7686389258582457602591798109664610559676104901531905534612371862156545682969746321939724950213366661636057536396779252859389632742413403244591187693751857699628584822959009920039586511918331032717466981617102477216955452515931265069265459682575124225929982484549136821686672341957090084798297901945350456714473246976282931047515059052131380350014617491424546432109112221506785196917078386726176965468588606774134572580668444740086109512807232439800764077947169834856997061535689836542138166769909236750987732240414274002288285785607256803383237379566639531930762047062673439517943372528066912105695847685374443102191667563509517486566769236505413400380565051983826496246388789426936587553197854928983707975272349056386817513728191815761344305079832337564878329836898161980996260364000073928407804100971048825945654928390119537091987437292216008763261326016208316985670
Im = 0.0014695398454686002602235602267435872742696288949454819641251917327001871646802222375794043554808984181050527747507024464475338925367544255504298138781497343514560484733471422567832875318623115371701089842454270266265594519203981996708780997969745056297187067310740754284635798427586526851073269358903637794497695778867387359644780106433549147575964695111500996174081311715975724522468033785608575894350758842715149520432125463466989127128011373497235051106233995040400616686607537287015952944156433221067736412912764567454009987622575582846143831794466663212601750260788535536819398196051616431301579942687208400722137429236421828930580251321137582633974441013377045265864719031580086405254319096195351614253832019998050137179725141523664399006493496816091681497072318461909569635448046827726248602343503824462069744543470519557285574917761743072242567051244893569548
Image size
4500x3375px 30.75 MB
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Comments7
anonymous's avatar
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SeryZone's avatar
SeryZoneHobbyist Photographer
Wow! This is amazing!
DinkydauSet's avatar
DinkydauSetHobbyist Digital Artist
Thank you! It's very hard to continue from here on. The shapes are so deep.
SeryZone's avatar
SeryZoneHobbyist Photographer
It require a lot of iterations, right?
DinkydauSet's avatar
DinkydauSetHobbyist Digital Artist
Not too many
It's mainly the depth that matters here.
SeryZone's avatar
SeryZoneHobbyist Photographer
Do you mean complexity?
DinkydauSet's avatar
DinkydauSetHobbyist Digital Artist
No, I mean depth. A first morphing of a julia set can be done at about 20 zooms. From there it's 50% extra depth for every step. At 15 steps we have about 8,758 zooms, and from there on it gets really difficult because of the time it takes to zoom. With 3rd order evolution, each of the 3 chosen shapes needs to be evolved, and with about 15 steps available, that is a big limiting factor.
SeryZone's avatar
SeryZoneHobbyist Photographer
Okay, I understood... 
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