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Description
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
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
