*Continued* SuperFractalThing: Arbitrary precision mandelbrot set rendering in Java.

[hapf]

Does that also include the newton-raphson iterations to find the exact location parameters, and the size of the minibrot?
For this, that requires high precision division, I use http://speleotrove.com/decimal/decnumber.html

I'm not familiar with that library. I use mpfr. Of course Newton is included. That is the main expense. The size I do
a different way, but it's a small factor in the running time.

[stardust4ever]

Finding the minibrot of period 82432 in the center takes "only" some 20 minutes.
But the time grows exponentially, more precision is required and period is equal to the number of iterations made.
55 minutes was to find the minibrot on the left of the leftmost X formation, with double period of 164864.
I estimate next doubling, i.e. the 4096X image of period 329728, to take about 5 hours.
I'll make a test-run of this tonight

Please do share the coordinates when you find it. This is awesome!

EDIT: I did a 25600x640 4x4 AA render of the 2048X formation in Mandel Machine.
http://sta.sh/028ljqxi5xf3

[Kalles Fraktaler]

So my Newton-Raphson is 10 times slower than hapf's. (20min vs 2min)
Might be that decNumber is slower than mpfr, but probably not 10 times slower.
I have also wrapped decNumber in a C++ class CDecNumber to be able to use simple arithmetic expressions, and by doing so I think more temporary variables are used (creation, allocation, initialization). Furhter I am using a class wrapping complex math.
But my code is available for download, this code is in the file newton.cpp.

Attached is the 4096X image 
The minibrot of 1024X, which was the original wish from stardust4ever, I think hapf can give it to us, in two minutes?

[stardust4ever]

So my Newton-Raphson is 10 times slower than hapf's. (20min vs 2min)
Might be that decNumber is slower than mpfr, but probably not 10 times slower.
I have also wrapped decNumber in a C++ class CDecNumber to be able to use simple arithmetic expressions, and by doing so I think more temporary variables are used (creation, allocation, initialization). Furhter I am using a class wrapping complex math.
But my code is available for download, this code is in the file newton.cpp.

Attached is the 4096X image  
The minibrot of 1024X, which was the original wish from stardust4ever, I think hapf can give it to us, in two minutes?

Ooooooo...

I'll download it later, thanks! How long did it take your program to locate the 4096 mini? Perhaps some optimization is in order? I feel almost guilty letting you find stuff while I relax. Beyond the 1024X formation, finding the centroid manually would be dang near impossible, and you must do it repeatedly with each new formation.

EDIT: My cores are burning a new render right now at 38400x640 4x4AA (60:1 aspect ratio, 153600x2560 native). Your sample file was off center so I had to locate centroid. Ironically, you zoomed into the wrong midget causing the center two Xs to be slightly closer together, making the centroid easier to identify, albeit this defect also messed with my OCD complex a bit. I wonder if the period of the 4096X mini will be perfectly divisible by 2048 as a result, or slightly off???

EDIT2: I attempted to upload my 38400x640 PNG image (26.7Mb) to deviantart. Error, DA does not accept submissions greater than 200 megapixels. But it's only 24.5 megapixels, not 200+ 

[Kalles Fraktaler]

I don't know how long time it took. I just started it and in the morning it was finished by I estimate it took 4-5 hours.
Sorry I missed the exact period (actually I saw that but I wondered if you would notice... And you did )
I should have stored the location where the leftmost x was in focus and examine the resulting period before continue. I'll do that next time
The result was far in the formation so I had to zoom out a bit. Next time I'll zoom out by changing parameters rather than using the mouse, so that it keeps the position of the center

[stardust4ever]

I don't know how long time it took. I just started it and in the morning it was finished by I estimate it took 4-5 hours.
Sorry I missed the exact period (actually I saw that but I wondered if you would notice... And you did )
I should have stored the location where the leftmost x was in focus and examine the resulting period before continue. I'll do that next time
The result was far in the formation so I had to zoom out a bit. Next time I'll zoom out by changing parameters rather than using the mouse, so that it keeps the position of the center

It's alright man. I counted dendrites everytime to be sure. Amazing that for my original XX Reactor Core and subsequent Magnum Opus Ex, I literally eyeballed the location between the arms every time, and although not perfect, it looked good enough. But my spiral arms in that sequence was much longer so that you could not actually see the interior cells within the chromosomes, meaning counting dendrites would have been more difficult. My first 32X formation on the way to the initial X of Xs formation had a slight gap between the center two chromosomes.

Do you have the period of the central minibrot in the 4096 formation? I'm curious as to how switching between midgets will impact the result. Since you appeared to zoom between the second dendrites rather than the third (and I am completely guessing here), maybe the period will be 2048 * 161 ±1? That would be something...

[claude]

So my Newton-Raphson is 10 times slower than hapf's. (20min vs 2min)
Might be that decNumber is slower than mpfr, but probably not 10 times slower.
I have also wrapped decNumber in a C++ class CDecNumber to be able to use simple arithmetic expressions, and by doing so I think more temporary variables are used (creation, allocation, initialization). Furhter I am using a class wrapping complex math.
But my code is available for download, this code is in the file newton.cpp.

Your newton.cpp looks very familiar to me!   Looking at the decNumber website it said "optimized for 10s of digits, but works for many more", while MPFR is highly optimized for a wider range of precisions.  Also, you probably don't need full precision for b and l in m_d_size(), which might speed it up quite a bit (no need for high precision division here, for example) - I'll try to experiment with this in my code later to see how it works.

[hapf]

Please do share the coordinates when you find it. This is awesome!

EDIT: I did a 25600x640 4x4 AA render of the 2048X formation in Mandel Machine.
http://sta.sh/028ljqxi5xf3

Location of 82432 minibrot
-1.7697392710757027841152006141906594654234779937259515247210119204006409471133661312119570293427350953111092082771973598855782759599980633037132375185987670114621045880606454417706999699982839165518556104246980851140230022353588311445547248451142336585544111916489341441418890633019730101854648463669109636471162672120817824917407218303348419898985242808140058964414457471465221536301689319210853379995524156624829942780946758964309072692484524503974031949154005423948971844113769257156823395255042997434557967120122936287886272994336827603988076644070845456535059390110455532123959338354686709501965947157116618024249418340042125809823163860665551942191883280150556503637746217516167947991343226606484863461721881250950867469305763323991190602711636193429181021868663451423240656141036481686672207216510178940927578426246138789051935948202201039069515784638090342979600881257471340705419667858851219685966190797231145977198268039243169238831169502470679242625047521216680080745102102338697978848434690710623615151918273912523550802047059388477608402978284517054069348844790654147973180174452501518676787305014157012005952675554689866176991833832220619238422806837710687818636075410966006549937218884711696E+00
4.795755933865217850561566322048697115430488688667392078125611175239810610728036667598929869177979713673736496183075852 37412544802866649204604791951282119532611555692231864126608560335395830677937445526989723059565598206590367891898467394 91155635838617923497250059314208186984179036223826655324004181421335633738898275114135499319014247271095039118772708132 30275054791364523084480643862835179727810155242098556813357886737442693746778591620701975874779407387049476510871738446 17863477560652949841356272962069000764292715737566241003234711235604702236267464602650182979303592890434112792457622396 98772188260974285993117734181827318766613834051977484272020698249213489627750957498023989747438133307647274695802671234 94383498158434263605620065563388355686765033779699309122944412035805072366352312023563970413682432326432420961714656976 36427613416621899589621369247195520694822931509253743782829062500391710822844657024864444608408422058560922524446048148 92208734287500540251296138686660257059365390928468879124177736053405984117806338296754892838258823127354280279919545995 57464102604534423229962807181907379443588506315493789312605325008852448399498815461778112569598868130991918320226621576 9426778203932399E-03
4.0E-1197
My size is not exact as I don't use the precise formula (yet). But the image will show the minibrot and not too small.

164864
-1.769739271075702784115200614190659465423477993725951524721011920400640947113366131211957029342735095311109208277197359885578275959998063303713237518598767011462104588060645441770699969998283916551855610424698085114023002235358831144554724845114233658554411191648934144141889063301973010185464846366910963647116267212081782491740721830334841989898524280814005896441445747146522153630168931921085337999552415662482994278094675896430907269248452450397403194915400542394897184411376925715682339525504299743455796712012293628788627299433682760398807664407084545653505939011045553212395933835468670950196594715711661802424941834004212580982316386066555194219188328015055650363774621751616794799134322660648486346172188125095086746930576332399119060271163619342918102186866345142324065614103648168667220721651017894092757842624613878905193594820220103906951578463809034297960088125747134070541966785886447235288609105205909051966704511390942958234951725775387781758459235336175874914270060330166029309002784046415623697961895242005503529241613049938875201316418805650345160787707082069430907259514732728631017193166465504703053934935961646564915133207244015482058441753719600349169975913355004239363576081672409151102056629192501261586962761927470258782581498100156087217125546233913570946909838442411747099090152522790702979685441760415183368490954812623454392070291588605339667563840849996394784933650758616925474283537172883193450082859567337887379500871669909017389638548162592153738613059110533772483733473275333867643410814003712668369348314058179792839355314227907424124598113218044738398444350897697621559901552501780149313577782153477162540804552586287234215857991922295263005128903584217506544184641753393387000976260838125827374281569957922478134436493538789174735905099046601671973696086709665874644202058E+00
4.795755933865217850561566322048697115430488688667392078125611175239810610728036667598929869177979713673736496183075852 37412544802866649204604791951282119532611555692231864126608560335395830677937445526989723059565598206590367891898467394 91155635838617923497250059314208186984179036223826655324004181421335633738898275114135499319014247271095039118772708132 30275054791364523084480643862835179727810155242098556813357886737442693746778591620701975874779407387049476510871738446 17863477560652949841356272962069000764292715737566241003234711235604702236267464602650182979303592890434112792457622396 98772188260974285993117734181827318766613834051977484272020698249213489627750957498023989747438133307647274695802671234 94383498158434263605620065563388355686765033779699309122944412035805072366352312023563970413682432326432420961714656976 36427613416621899589621369247195520694822931509253743782828991308508271169923822030731210535571166710661634286964536828 24916625524427139390115841789048084223745126926476087976333742845383690477681495551638402916197904734052582284850369170 28783885294577276496108004745400971309479389147687770693906539073866265982191975377071034728527739284879540225761730903 00830083242555816576865669179621054197697073306371497138708514154639978238654075859456762116645947307361805048300920909 05114405486371454167740496277753504637822001344505953585271524767086934467673307415924294721749272608918042101324755774 29262372746433308021144056437236809826934936780650803210549920958407471657473426515989075764687564059576769732394643948 98303249003035346570430635955169214125771039539353732135890401126564177895335144578423771521555862079611886138494457318 93059515732843156829587178656534745871092434334209161871719965573648858166477124178175985395683928887677055734604068148 66255396048362201824987106E-03
8.0E-1801

329728
-1.769739271075702784115200614190659465423477993725951524721011920400640947113366131211957029342735095311109208277197359885578275959998063303713237518598767011462104588060645441770699969998283916551855610424698085114023002235358831144554724845114233658554411191648934144141889063301973010185464846366910963647116267212081782491740721830334841989898524280814005896441445747146522153630168931921085337999552415662482994278094675896430907269248452450397403194915400542394897184411376925715682339525504299743455796712012293628788627299433682760398807664407084545653505939011045553212395933835468670950196594715711661802424941834004212580982316386066555194219188328015055650363774621751616794799134322660648486346172188125095086746930576332399119060271163619342918102186866345142324065614103648168667220721651017894092757842624613878905193594820220103906951578463809034297960088125747134070541966785886447235288609105205909051966704511390942958234951725775387781758459235336175874914270060330166029309002784046415623697961895242005503529241613049938875201316418805650345160787707082069430907259514732728631017193166465504703053934935961646564915133207244015482058441753719600349169975913355004239363576081672409151102056629192501261586962761927470258782581498100156087217125546233913570946909838442411747099090152522790702979685441760415183368490954812623710090511242543608917349145489460218746793257338764367911285022883289062897447549864531670593639618293269919754424328199154461642505051474442950545512129612065538480436754189449243374455402063695195911267548833679802317275576476188543915475031364789399273115233379038627421088649020855711068234548337133910087974623387870195080066953919247961134181399464234373015837145112272610289097131091363912594607674348025596742166815160833789499510195821035859427778879593741772710817354555659829656706186885840812135338916553030076217012227562330543876469277608752973750164067876151245246259233381866230803348292290715834776568338009333475980843926459331892128780025573957692815238898466113022389848052053459522940406362857290067326891576631387464304793863617338320930824299047936065382705961860281865056902721884419223186529234893321540873195951071305612876439032604008291124876981974861633925782863084453524979923319564608387116832010057792691825272273903303402371563704744315198700910908844377944687296050041369717545265216393499672031992190943889616208372772553048963841081795026179698770958421574168437073984204125293513662359529913580852507804462311103835669649604439882040825600879568687357873533973193667508999150210175297730647460519426766598089591461498779912853983510872928739258345215721655413389930269090956885498898449199249910988493703064733865389752445354408708811E+00
4.795755933865217850561566322048697115430488688667392078125611175239810610728036667598929869177979713673736496183075852 37412544802866649204604791951282119532611555692231864126608560335395830677937445526989723059565598206590367891898467394 91155635838617923497250059314208186984179036223826655324004181421335633738898275114135499319014247271095039118772708132 30275054791364523084480643862835179727810155242098556813357886737442693746778591620701975874779407387049476510871738446 17863477560652949841356272962069000764292715737566241003234711235604702236267464602650182979303592890434112792457622396 98772188260974285993117734181827318766613834051977484272020698249213489627750957498023989747438133307647274695802671234 94383498158434263605620065563388355686765033779699309122944412035805072366352312023563970413682432326432420961714656976 36427613416621899589621369247195520694822931509253743782828991308508271169923822030731210535571166710661634286964536828 24916625524427139390115841789048084223745126926476087976333742845383690477681495551638402916197904734052582284850369170 28783885294577276496108004745400971309479389147687770693906539073866265982191975377071034728527739284879540225761730903 00830083242555816576865669179621054197697073306371497138708514154639978238654075859456762116645947307361805048300920909 05114405486371454167740496277753504637216725435211947686690717207242268279427062224063162157529921214604449515145333485 69697163947410860260042883945538333531867769572754496263728994570997655115727544947304655776134821781071432315077788681 93423822555039917522330571396889048290104744980464581866770334921864862190266138471198274482010210168316288917311981835 98293088638858711567120968177302873251999501276374450163902450481515972523418359944973605551138606416972280896996253069 20034682736487389472930049460779570255081356003065703425429406501150693392757174029256410860513000350138657898547495198 60970433307909167319792093324658408940088668436478021343464689378290662880864663036666289243225104846172650503844946615 93822786005863096074096988012554285208824809751306036128329950587835108205840064550189661056811559904010130757210069506 27190231016944759817240462704955514975031195066427207347197603388970387505837250901691346557551255520037069779877707927 76269792500678216496903521911500152926760572350990813834249475429067175023071726399813724479068890226360989110145376714 36110958254082603126359686713114884125214839162294452032294422326966181126948955205441251450291494114791213610990437840 86682825047148661008899020485879940592842198570843905373549040081151368303374112743502357124213109285192023209397856498 927549535788406353730878501858992074668205181907450423668960254535346712772096404311351455809816966666E-03
7.0E-2710

[Kalles Fraktaler]

hapf, how much precision do you use for the 3 steps?
I used double exponent + 20, for example if magnification is 1e100 I used precision 220, since the minibrot you want to find when you are at e100 is found around e200.
I realize this is a big exaggeration when finding the period, and when I tried use something like exponent + 4, I succeeded reducing the time from 1 hour to 10 minutes for finding the 329728th period.
The same applies for finding the minibrot size.
But what about the Newton-Raphson iterations?

[stardust4ever]

Location of 82432 minibrot
[...]
My size is not exact as I don't use the precise formula (yet). But the image will show the minibrot and not too small.

164864
[...]
8.0E-1801

329728
[...]

Nice. Thanks for publishing the coordinates. I've just finished making renders based on the "X of Xs" extension on the 1024X and 2048X patterns. I've come to the conclusion in this situation that less is more. The 1024X^2 pattern is more visually pleasing than the 2048X^2 or the 4096X^2 patterns. Ive just rendered a 4800x4800 sized image of the 1024X^2 formation (each arm has 512 chromosomes for a total 2048) in Mandel Machine with 4x4 Antialias (19200x19200 native). I had two renders going at once but it finished in less than 40 or so. I did not record the render time. Sure beats waiting for months like in the old days...

UPDATE: http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/reactor-core-ii-long-extended/msg91254/#msg91254

hapf, how much precision do you use for the 3 steps?
I used double exponent + 20, for example if magnification is 1e100 I used precision 220, since the minibrot you want to find when you are at e100 is found around e200.
I realize this is a big exaggeration when finding the period, and when I tried use something like exponent + 4, I succeeded reducing the time from 1 hour to 10 minutes for finding the 329728th period.
The same applies for finding the minibrot size.
But what about the Newton-Raphson iterations?

That's quite a reduction in time by reducing the precision. The trick is figuring out the lowest precision you can get away with for a given location without borking the image or computation.

[hapf]

hapf, how much precision do you use for the 3 steps?
I used double exponent + 20, for example if magnification is 1e100 I used precision 220, since the minibrot you want to find when you are at e100 is found around e200.
I realize this is a big exaggeration when finding the period, and when I tried use something like exponent + 4, I succeeded reducing the time from 1 hour to 10 minutes for finding the 329728th period.
The same applies for finding the minibrot size.
But what about the Newton-Raphson iterations?

You need the max abs difference of the exponents of involved numbers plus the bits for actual computations (about 64 and more). So for Newton it changes dynamically with the deltas computed. Using more bits than neeeded was likely the main reason you were much slower.

[claude]

Also, you probably don't need full precision for b and l in m_d_size(), which might speed it up quite a bit (no need for high precision division here, for example) - I'll try to experiment with this in my code later to see how it works.

Yep, the size algorithm works fine with b and l at 53 bits (so you could use extended double, not sure if double has enough exponent range here for deep minibrots), but z still needs full precision or you get bad results (how bad depends on how insufficient the precision is for the nucleus - can be a factor of a few 10s out, or much worse).  Your precision for minibrot looks about right I think, but the box period algorithm can make do with just the precision needed for the current view.

[hapf]

Here's a stardust4ever inspired location for your enjoyment. 

3.589641819829216607382609417707637501320749736599154187388156131262748633869720822102177100684166384145148327222689692 81488472407713155528345630704397417629670141110343170021721243757862646913901724545557060305164312180572254270986148389 59699368414675461998880249824565358234199284816122514292968303287346941310883255068644748074235559844802361435070498424 76526320116940586102672644826449938957783213094447195870362481455087226981524375556463246790978877939104974306759373654 95926868711176329970158813919842855781966304322941328563470672649835624313526503289759397615067366095073366638976613939 91053194884997066273036879409031967424512605175625111404211004144201249692853502015985612267872774541652491754754314221 20442479566766096374590170397985550548732406192212509063291992458610079232291946402423127151934651249247124593283076362 45689208991069282426422419901048427981761053143859632625842877434724756333636907669055033915059410143035962114836789002 1324294424168028670423525633418320025E-01
6.466670689777818471393024431453617731923847636419096970436633765407118059261810323272531697149210641561475145206899728 71390150695198587931606814482611490152723459684882730977059760038778133624338908343616998166488064800949328057501799440 60613108429195582449318242145813771930544484511788530467939993254684631925285391042706019498861457258147124466018368775 41315036835282952490756339100025232304644872081673629835710372300539925650667991602461845152324404502028158770953659501 62059820358633620871598958692529172113978947975464568215722988428558030334721223368913598969236580810803654649883636804 77086764974930105230400256420038951316574886116088454897889563727196824656125261469899519180134721371611896240819622553 32241748593258884044426820533406476454959343547969342125823929289523458306897581652466915315243113920948043450777960395 46530870503869617628545499870873124406583289807206160443088359970121647971308105278105739704155382549737732546138531492 3187346016701118771263346391791002905E-01
2.5E-649

[stardust4ever]

Here's a stardust4ever inspired location for your enjoyment.  

3.589641819829216607382609417707637501320749736599154187388156131262748633869720822102177100684166384145148327222689692 81488472407713155528345630704397417629670141110343170021721243757862646913901724545557060305164312180572254270986148389 59699368414675461998880249824565358234199284816122514292968303287346941310883255068644748074235559844802361435070498424 76526320116940586102672644826449938957783213094447195870362481455087226981524375556463246790978877939104974306759373654 95926868711176329970158813919842855781966304322941328563470672649835624313526503289759397615067366095073366638976613939 91053194884997066273036879409031967424512605175625111404211004144201249692853502015985612267872774541652491754754314221 20442479566766096374590170397985550548732406192212509063291992458610079232291946402423127151934651249247124593283076362 45689208991069282426422419901048427981761053143859632625842877434724756333636907669055033915059410143035962114836789002 1324294424168028670423525633418320025E-01
6.466670689777818471393024431453617731923847636419096970436633765407118059261810323272531697149210641561475145206899728 71390150695198587931606814482611490152723459684882730977059760038778133624338908343616998166488064800949328057501799440 60613108429195582449318242145813771930544484511788530467939993254684631925285391042706019498861457258147124466018368775 41315036835282952490756339100025232304644872081673629835710372300539925650667991602461845152324404502028158770953659501 62059820358633620871598958692529172113978947975464568215722988428558030334721223368913598969236580810803654649883636804 77086764974930105230400256420038951316574886116088454897889563727196824656125261469899519180134721371611896240819622553 32241748593258884044426820533406476454959343547969342125823929289523458306897581652466915315243113920948043450777960395 46530870503869617628545499870873124406583289807206160443088359970121647971308105278105739704155382549737732546138531492 3187346016701118771263346391791002905E-01
2.5E-649

I like your dots!

In other news, I'm making excellent progress in my KF zoom movie. Unfortunately, I found a couple of glitch frames in my Kalles Fraktaler zoom movie of the 1024X Long location. At the edge of the 512 formation exactly at the halfway mark, part of the image renders incorrectly.

I think I may just upload the rendered AVI files to youtube as is, rather than attempt to correct the glitches. I'm using Fibonacci numbers for the infinite waves but I may chose a slightly less dense set of numbers for the AVI files. Also sadly I got a copystrike on YT for a gameplay video I did, so now I'm limited to 15 minute uploads for the forseeable future, and it will either play back either at ludicrus speed (6 frames per 2x zoom) or I will have to parse it into 2 or 3 separate 15-minute videos. I can splice it into two pieces (>30 minutes) if I do 12 or 13 frames per zoom...

[cKleinhuis]

hehe, that glitch looks like a sword