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rope 5e-900Mandelbrot set for f(z)=zē+c
rope 5e-900
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Description: Continuous iteration count coloured with "pseudo-distance-estimate" (based on gradient of iteration count).

Perturbation references calculated using MPFR for arbitrary precision floating point, with Newton's method to find new references to rebase glitched pixels when glitches are detected.  Deltas from the reference use extended precision long double to avoid exponent underflow.

Most of the code is C99 with OpenMP parallelization pragmas generated by a program written in Haskell, pthreads also distribute the work to multiple threads in a queue prioritised by the number of pixels needing each reference point.  The main program uses GLFW3 for the user interface, requiring OpenGL 2.1.

Series approximation uses 24 coefficients, cached for each exponent as long as the primary reference point is valid (close to the viewport) - zooming deeper only needs to calculate the extra iterations for the series.

Zoom technique: find an embedded Julia set, morph it into a tree, then an S, and then stripe of Ss.  The exponent at each manual morph decision point was roughly 1.5 times larger than the previous one.

Render time from scratch (no cached series approximation coefficients): 2h25m CPU time, spread over 4 cores.

Coordinates (also present in the PNG comment of the image):
Code:
real=-1.9999999991382701187664867263777990802315521777725699896559744332163282809190635876338689862252325486275625176234228599345356271638886256134858501887192790542028024935049951885407761891767298885150806301222775248925838511719275938509741075480277121921782935196497935309735482091452620516406034458393098999647940401559938022277208796123426942890238548831242642214390832843663278956233050479434756210424758074063274012884699785015713030693196664115930787808873909835082875486167322692191083088951521662394670382361640378899078207636966502200823315829897334623853239814830789027165894348552076936531680735018255850564942605475860412736727968473542239467786774761949850136542501097226763334458574697769205393465539695021109807324946639132668217325174136197587426527792772488452306526998495228499255820559468584627950009868491445852416867477767407138072890406102328444390308998869827191574700401134779144435335084576208608e+00
imag=5.4737655329230406244271237478004609407066488694580295427082121408648049051968347457532505196983460439747136933981356733123108522845595812535279088637906242300707715181703346635608401442786224018063857573459378429940709218143100603065686995530121072747340660182011443571732142526400428501016008337666314885447794156074780085580855962001303264064438172268797637297148218624160052530221780539761474767504612768556791208553163830221520758230484827443972845481581643582599593218102983020711688648349114250987759017516818299106792776958539806226515640144132951537057032176096824936409811037266760614805078065187070352947835163348804509613578525292574005998946394238930178306443929221654818682601799458479995018433479582270955818971685110188454320364119024820370323482104975364360877373269389038265094020494024196483674915643479481590748408113211854384934420560040206494997345159079315914533591630770590420769600290109583975e-20
radius=5e-900


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Total Favorities: 0 View Who Favorited
Filesize: 721.45kB
Height: 720 Width: 1280
Keywords: mandelbrot minimal rope 
Posted by: claude June 11, 2015, 03:17:09 AM

Rating: **** by 1 members.

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