Fractals/gnofract

Images :commons:Category:Fractals created with Gnofract4D frc files A repository of formulas used to generate and color fractals. This repository contains formulas which are compatible with the Gnofract 4D fractal generator. Many are also compatible with FRACTINT https://www.fractint.org/ and with UltraFractal https://www.ultrafractal.com . #!/usr/bin/env python # gnofract4d /gnofract4d-3.13/fract4d/parfile.py # rudimentary read-only support for Fractint PAR files # issues discovered while looking at fotd3.par # y needs to be negative (?) # use gf4d.cfrm#default - continuous potential doesn't work? # rotation == -xyangle in degrees, needs convert to radians import string import preprocessor import math def parse(file,f): # reset the fractal to have defaults closer to Fractint f.set_outer("gf4d.cfrm","default") f.yflip = True params = get_params(file) pairs = get_param_pairs(params) formulaname = pairs.get("formulaname","Mandelbrot") formulafile = pairs.get("formulafile","gf4d.frm") f.set_formula(formulafile, formulaname) for (k,v) in pairs.items(): if k == "maxiter": parse_maxiter(v,f) elif k == "center-mag" : parse_center_mag(v,f) elif k == "colors" : parse_colors(v,f) elif k == "params" : parse_params(v,f) elif k == "logmap" : parse_logmap(v,f) def parse_params(val,f): paramlist = val.split("/") l = len(paramlist)/2 for i in xrange(l): (re,im) = (paramlist[i*2],paramlist[i*2+1]) name = "@p%d" % (i+1) val = "(%s,%s)" % (re,im) f.forms[0].set_named_param(name,val) def get_params(file): return preprocessor.T(file.read()).out().split() def parse_logmap(val,f): f.set_outer("fractint.ucl","outside") f.forms[1].set_named_param("@logmap",val) def get_param_pairs(params): pairs = {} for p in params: vals = p.split("=") if len(vals) == 2: pairs[vals[0]] = vals[1] return pairs def parse_maxiter(val,f): max = int(val) f.maxiter = max def parse_colors(val,f): colors = colorRange(val) f.get_gradient().load_fractint(colors) def parse_center_mag(val,f): "x/y/mag(/xmag/rot/skew)" vals = val.split("/") x = float(vals[0]) y = -float(vals[1]) mag = float(vals[2]) f.params[f.XCENTER] = x f.params[f.YCENTER] = y h = 2.0/mag f.params[f.MAGNITUDE] = h * 1.33 if len(vals) > 3: xmag = float(vals[3]) if len(vals) > 4: rot = float(vals[4]) * -1 * math.pi / 180.0 f.params[f.XYANGLE] = rot if len(vals) > 5: skew = float(vals[5]) def setup_log_table(log_flag, maxltsize, colors, save_release): # try to match convoluted Fractint log_table logic (lf,mlf) = get_log_table_limits(log_flag, maxltsize, colors, save_release) table = [ calc_log_table_entry(x,log_flag,lf,mlf, save_release) \ for x in xrange(maxltsize) ] return table def calc_log_table_entry(n, log_flag, lf,mlf, save_release): if log_flag > 0: if n <= lf: return 1 try: if (n-lf) / math.log(n - lf) <= mlf: if save_release < 2002: if lf: flag = 1 else: flag - 0 return n - lf + flag else: return n - lf except ZeroDivisionError: pass return int(mlf * math.log(n - lf)) + 1 return 0 def get_log_table_limits(log_flag, maxltsize, colors, save_release): if save_release > 1920: if log_flag > 0: lf = log_flag if log_flag < 1: lf = 0 if lf >= maxltsize: lf = maxltsize -1 if lf != 0: delta = 2 else: delta = 1 mlf = (colors - delta ) /math.log(maxltsize - lf) return (lf,mlf) def decode_val(c): if c >= '0' and c <= '9': return 4 *(ord(c) - ord('0')) elif c >= 'A' and c <= 'Z': return 4 * (ord(c) - ord('A') + 10) elif c == '_': return 4 * 36 elif c == '`': return 4 * 37 elif c >= 'a' and c <= 'z': return 4 * (ord(c) - ord('a') + 38) else: raise RuntimeError, "Invalid character %s in colors" % c def colorRange(s): '''From help4.src: The colors= parameter in a PAR entry is a set of triplets. Each triplet represents a color in the saved palette. The triplet is made from the red green and blue components of the color in the palette entry. The current limitations of fractint\'s palette handling capabilities restrict the palette to 256 colors. Each triplet rgb component is a 6 bit value from 0 to 63. These values are encoded using the following scheme: rgb value => encoded value 0 - 9 => 0 - 9 10 - 35 => A - Z 36 - 37 => _ - ` 38 - 63 => a - z In addition, Pieter Branderhorst has incorporated a way to compress the encoding when the image has smooth-shaded ranges. These ranges are written as <nn> with the nn representing the number of entries between the preceeding triplet and the following triplet.''' colors = [] i = 0 runlength = 0 while i < len(s): c = s[i] if c == '<': j = string.find(s,">", i) if j == -1: raise RuntimeError, "No > after < in colors" runlength = string.atoi(s[i+1:j]) if runlength == 0: raise RuntimeError, "Zero runlength" i = j+1 else: if len(s) < i+3: raise RuntimeError, "invalid color string" rgb = map(decode_val, list(s[i:i+3])) if runlength > 0: if len(colors) == 0: raise RuntimeError, "run with no preceding color" pairs = zip(colors[-1],rgb) for k in range(0,runlength): ratio = (k+1.0) / runlength nratio = 1.0 - ratio col = map(lambda (x,y) : int(x * nratio + y * ratio), pairs) colors.append(col) colors.append(rgb) i += 3 runlength = 0 return colors if __name__ == "__main__": import sys import fc import fractal g_comp = fc.Compiler() g_comp.add_func_path("../formulas") g_comp.load_formula_file("gf4d.frm") g_comp.load_formula_file("test.frm") g_comp.load_formula_file("gf4d.cfrm") f = fractal.T(g_comp) file = open(sys.argv[1]) parse(file,f) f.save(open("parfile.fct","w")) Period checking cpp code c and mpfr code Coloring algorithms /* https://github.com/edyoung/gnofract4d/blob/master/formulas/standard.ucl comment { This file contains standard coloring algorithms for Ultra Fractal 3. Many of the coloring algorithms here were written by other formula authors, as noted in the comments with each formula. All formulas have been edited and simplified by Frederik Slijkerman. } */ Triangle { ; ; Variation on the Triangle Inequality Average coloring method ; from Kerry Mitchell. The smoothing used here is based on the ; Smooth formula, which only works for z^n+c and derivates. ; ; Written by Damien M. Jones ; init: float sum = 0.0 float sum2 = 0.0 float ac = cabs(#pixel) float il = 1/log(@power) float lp = log(log(@bailout)/2.0) float az2 = 0.0 float lowbound = 0.0 float f = 0.0 BOOL first = true loop: sum2 = sum IF (!first) az2 = cabs(#z - #pixel) lowbound = abs(az2 - ac) sum = sum + ((cabs(#z) - lowbound) / (az2+ac - lowbound)) ELSE first = false ENDIF final: sum = sum / (#numiter) sum2 = sum2 / (#numiter-1) f = il*lp - il*log(log(cabs(#z))) #index = sum2 + (sum-sum2) * (f+1) default: title = "Triangle Inequality Average" helpfile = "Uf3.chm" helptopic = "Html/coloring/standard/triangleinequalityaverage.html" param power caption = "Exponent" default = 2.0 hint = "This should be set to match the exponent of the \ formula you are using. For Mandelbrot, this is 2." endparam param bailout caption = "Bailout" default = 1e20 min = 1 hint = "This should be set to match the bail-out value in \ the Formula tab. Use a very high value for good results." endparam } References