Hello,
over the last days I experimented with my own fractal programm.
Currently I'm using only formula (1) from the sft document.
All calculations are done with long double 80 bit datatype, except the calculation of the reference point, where the GMP ist used.
Using the pertubation method now I found an error which I can't solve so far.
My current strategy is that I render small preview images with classic method to find/serch the destination. From the final image (with the minibrot) I compute the reference point and store the coefficients to a file.
The coordinates of the last image (attachment zp49_02989.jpg) :
mag=2.88024294864E2898
re=-0.228155493653961819214572014099126006737398351174508032379597981084415663036013066757421042711970437268939585386816469905360621768338929494238545390547353638503609151421208524788914955240718294649807399935999858816761369110006545501557947692511511536454828040448704636885667280398091611692374593524757189049141208420826812720100422874424982340170961075331068635883166081123269331016270098508361087077833154904324128264646204875932111444055804466980483012672723385931778337635951396292680216269878880929835721290940928138383036870128422877754678479378687051458498619808443944509984422719612504135983526148008466137865522665206222773200779260364022367950008156274210921001880108008314196073519829157791111634729470143710974893284477142277011069100090989918573842548583093041902409948263341207430845320627499806440266007807543988047999738958151286666046206551168115350844720738507133334406506452653595940075715923094608687884106538641949638234295555296508465577821151329306573686581379031862139316537865731512838172855479903298991578351489606840726611917981648696455854495480128253062002382824250864806171913970931008751474727225679181892630170444822162895840361277130105613864721353386423980667073024401175253401896396788209829755777820245161381601753515409160039758973533401181997278485827483182910166596719767738728693166928637632784068782877190200295915254857274809471379496091646052013653639158342906746821293477913861568838883162508227904940592508445082832451094658206070098108058371499803649262117527097081413044083361371066562956251606064550396670436453133336843005979891413645252634762472806536140083325083138834362873191797281507404788371661076451637908700257130578425313739088067922629601851900202306008656761349160170558054821783077427764971183638001976349030976540281059522366013490521318344494287825685683972005527548036903310243006117066821357863163417718657147681576891356822300948581194675279315162224403341879221739693797168925504499853355954355097038417524184580534783324042600624855594990648364249951166541789910527250646087684769157019315871077158701215895802129773414646582733370820644962213082363328203580749681294300016115452252455780732890426284986018411506856737674248839731009232410619262857692323992181178234570681591072148145279796792612534059038350091094969036678923079241620953258130319909153216181918642707776439297254842289395124971560595103914480136002250360380366789164501164021379143331637487422735109296178368448899890272880744288366530693237328421749021060696378904658674381112889857888727687242477971774241610970182520730551962045872256188999246396137554806824561283588046355838032402489833186295579971346325691464314115816938957352245127984517726729703131805459280137083921764482057913128936333458972465378578968319882929449933370450102446539616181407642051022841037512367677547833701068597069387195752871063339289690965027892986185709373603425376298321308954932257916427885866623571044189454
im=1.1151425080399373597457646363150140681887780904679546036274680334810409092946355168572572006874765228872100322451033324674089490817457188452599842530139888003789611498451538187135582267447926710194039382369014758821696953203973909890684815787539535821296738902997986221240372961651516963059575999816402095033448363132460536005643111932958088293412160670689807879737489438573051324049431610845845747954843962673151100894218512451430034482302328794196056334954411558991905342112112527527903101934319426939125067685400406793219409258237634837567486913882656202820651153459408007214812446063004016990478652901305445641122501686263488595219535793985626639534336539014265204709419139006829819188034750141155411193942246951711574277826630794139256362861546610055511351508465695050691949963483822796221939931284629304822712266585418510537313581792664669885462998369057457995067178653752112010687171006981485870807732922069316869110790300072072961715073179740733857227860008589343847074244422121264906898067851895317160951594245327166628108445186252755952562820517988653414929514419637982778276100132099044433881697905459607257608704571044608840074600309371170216417153702491354786271482917736397381910879181445890339571901612161824780067385824034904436695525460581789870754064314359375849781174311237014600685868261161702827885199481741564438007098545323618020438796286585378653666144021361273489608750774381256160101950998522642093298816512318824240203295362977204772074460983061335733453289220960361273409315843918512887588053023715941861535225775429375759015715633393748709688013165752203810756242094878573353612094730613240777870652441806811252784643578997978414892546008070868023070747066206136774534412629745372683863679282378169357137066484245197250072336080141492007754525005486530094823130207333560286412822695456193472387286376424371240431060509001478621687281443210037065314193343618601793870015025387509766440356455882647611930693616127361505861471995759634443772740541616692106177742144352735744095844199462629413973080316955741894123134334902602570947329407545843053855340696592190717100838849013734180856505792043366349580277646631461376896978255186945840215922875749111283561204003335890235067985143510968326747002049195838337080988192303737065403326741832397443406356733892505198041781305606875612762932951292773275293846272679425063624136210734658811593428349846101949855305243090175870138182920684489434323316137210867670470427033067914111333436480844643340923940374500495312223151203285993936839272213248991819604992074915090477549511648617468307425977988429768060170998567455827405676228064241314809243394200295517516898896908251562377157190452790952630454750281401919398985141306754952210761711380933635198919292677892763674067677938401345844814645204200417440700040927453875886834756769956564930870727588540356647641850358821048775347902381456140582213325789250363676047238936614189747321052837198997491256584375
The coefficients file looks like this:
1 -1.419643377607080481084267376e+00 6.062907292071992859661122566e-01
2 1.419643377607080481084267376e+00 -6.062907292071992859661122566e-01
3 1.419643377607080481084267376e+00 -6.062907292071992859661122566e-01
4 1.419643377607080481084267376e+00 -6.062907292071992859661122566e-01
...
Then I reuse this values for computing all frame for the animation.
My problem ist now, when I reach (approx) zoom level 1.0E+1400, the classic rendered and pertubation renderes images get different.
Some details are going lost ans it seems that the pertubation redered images are auto-centered to a minibrot ?!?
Image parameters, where I get first differences:
Mag=1.0E1350
re=-0.228155493653961819214572014099126006737398351174508032379597981084415663036013066757421042711970437268939585386816469905360621768338929494238545390547353638503609151421208524788914955240718294649807399935999858816761369110006545501557947692511511536454828040448704636885667280398091611692374593524757189049141208420826812720100422874424982340170961075331068635883166081123269331016270098508361087077833154904324128264646204875932111444055804466980483012672723385931778337635951396292680216269878880929835721290940928138383036870128422877754678479378687051458498619808443944509984422719612504135983526148008466137865522665206222773200779260364022367950008156274210921001880108008314196073519829157791111634729470143710974893284477142277011069100090989918573842548583093041902409948263341207430845320627499806440266007807543988047999738958151286666046206551168115350844720738507133334406506452653595940075715923094608687884106538641949638234295555296508465577821151329306573686581379031862139316537865731512838172855479903298991578351489606840726611917981648696455854495480128253062002382824250864806171913970931008751474727225679181892630170444822162895840361277130105613864721353386423980667073024401175253401896396788209829755777820245161381601753515409160039758973533401181997278485827483182910166596719767738728693166928637632784068782877190200295915254857274809471379496091646052013653639158342906746821293477913861568838883162508227904940592508445082832451094658206070098108058371499803649262117527097081413044083361371066562956251606064550396670436453133336843005979891413645252634762472806536140083325083138834362873191797281507404788371661076451637908700257130578425313739088067922629601851900202306008656761349160170558054821783077427764971183638001976349030976540281059522366013490521318344494287825685683972005527548036903310243006117066821357863163417718657147681576891356822300948581194675279315162224403341879221739693797168925504499853355954355097038417524184580534783324042600624855594990648364249951166541789910527250646087684769157019315871077158701215895802129773414646582733370820644962213082363328203580749681294300016115452252455780732890426284986018411506856737674248839731009232410619262857692323992181178234570681591072148145279796792612534059038350091094969036678923079241620953258130319909153216181918642707776439297254842289395124971560595103914480136002250360380366789164501164021379143331637487422735109296178368448899890272880744288366530693237328421749021060696378904658674381112889857888727687242477971774241610970182520730551962045872256188999246396137554806824561283588046355838032402489833186295579971346325691464314115816938957352245127984517726729703131805459280137083921764482057913128936333458972465378578968319882929449933370450102446539616181407642051022841037512367677547833701068597069387195752871063339289690965027892986185709373603425376298321308954932257916427885866623571044189454
im=1.1151425080399373597457646363150140681887780904679546036274680334810409092946355168572572006874765228872100322451033324674089490817457188452599842530139888003789611498451538187135582267447926710194039382369014758821696953203973909890684815787539535821296738902997986221240372961651516963059575999816402095033448363132460536005643111932958088293412160670689807879737489438573051324049431610845845747954843962673151100894218512451430034482302328794196056334954411558991905342112112527527903101934319426939125067685400406793219409258237634837567486913882656202820651153459408007214812446063004016990478652901305445641122501686263488595219535793985626639534336539014265204709419139006829819188034750141155411193942246951711574277826630794139256362861546610055511351508465695050691949963483822796221939931284629304822712266585418510537313581792664669885462998369057457995067178653752112010687171006981485870807732922069316869110790300072072961715073179740733857227860008589343847074244422121264906898067851895317160951594245327166628108445186252755952562820517988653414929514419637982778276100132099044433881697905459607257608704571044608840074600309371170216417153702491354786271482917736397381910879181445890339571901612161824780067385824034904436695525460581789870754064314359375849781174311237014600685868261161702827885199481741564438007098545323618020438796286585378653666144021361273489608750774381256160101950998522642093298816512318824240203295362977204772074460983061335733453289220960361273409315843918512887588053023715941861535225775429375759015715633393748709688013165752203810756242094878573353612094730613240777870652441806811252784643578997978414892546008070868023070747066206136774534412629745372683863679282378169357137066484245197250072336080141492007754525005486530094823130207333560286412822695456193472387286376424371240431060509001478621687281443210037065314193343618601793870015025387509766440356455882647611930693616127361505861471995759634443772740541616692106177742144352735744095844199462629413973080316955741894123134334902602570947329407545843053855340696592190717100838849013734180856505792043366349580277646631461376896978255186945840215922875749111283561204003335890235067985143510968326747002049195838337080988192303737065403326741832397443406356733892505198041781305606875612762932951292773275293846272679425063624136210734658811593428349846101949855305243090175870138182920684489434323316137210867670470427033067914111333436480844643340923940374500495312223151203285993936839272213248991819604992074915090477549511648617468307425977988429768060170998567455827405676228064241314809243394200295517516898896908251562377157190452790952630454750281401919398985141306754952210761711380933635198919292677892763674067677938401345844814645204200417440700040927453875886834756769956564930870727588540356647641850358821048775347902381456140582213325789250363676047238936614189747321052837198997491256584375
Image classig rendered: zp49_1350.jpg
Image pertubation rendered: zp49_1350a.jpg
In the pertubation rendered image are two differences:
- the center is different, and all following images are different too.
- the zoom should pass the spiral, but the pertubation rendered images are centered.
I've done a second zoom with nearly the different result.
Also I wrote my program new from scratch also with the same result (if needed, I can post the code or parts of it).
I've no Idea what is going wrong
- reusing one reference point for all images
- is long double precise enough
- hardware defect
??
Had anyone else similar problems and give me a hint ?
Jürgen