# Fractals/ultrafractal

UltraFractal is a program by Frederik Slijkerman

## Contents

# licence[edit]

Copyright © 1997-2017 Frederik Slijkerman

# install[edit]

## Linux[edit]

use wine

# Help[edit]

- file types
^{[1]} - Fractal Forum
^{[2]}

# formula[edit]

## outside coloring[edit]

- Average Colorings

### ExponentialSmoothing[edit]

ExponentialSmoothing { ; from Standard.ucl ; This coloring method provides smooth iteration ; colors for all fractal types, convergent or ; divergent (or both). It combines the two methods ; developed by Ron Barnett. It doesn't map ; precisely to iterations, but it's close. ; ; Written by Damien M. Jones ; init: float sum = 0.0 float sum2 = 0.0 complex zold = (0,0) loop: IF (@diverge) sum = sum + exp(-cabs(#z)) ENDIF IF (@converge) sum2 = sum2 + exp(-1/cabs(zold-#z)) ENDIF zold = #z final: IF (|#z - zold| < 0.5) ; convergent bailout. IF (@converge) #index = sum2 ELSE #index = 0 ENDIF ELSE ; divergent bailout. IF (@diverge) #index = sum * @divergescale ELSE #index = 0 ENDIF ENDIF default: title = "Exponential Smoothing" helpfile = "Uf*.chm" helptopic = "Html/coloring/standard/exponentialsmoothing.html" $IFDEF VER50 rating = recommended $ENDIF param diverge caption = "Color Divergent" default = FALSE hint = "If checked, points which escape to infinity will be \ colored." endparam param converge caption = "Color Convergent" default = TRUE hint = "If checked, points which collapse to one value will be \ colored." endparam param divergescale caption = "Divergent Density" default = 1.0 $IFDEF VER40 exponential = true $ENDIF hint = "Sets the divergent coloring density, relative to the \ convergent coloring. If set to 1.0, they will use \ the same color density." endparam }

### smooth[edit]

Smooth(OUTSIDE) { ; from Standard.ucl ; This coloring method provides smooth iteration ; colors for Mandelbrot and other z^2 formula types ; (Phoenix, Julia). Results on other types may be ; unpredictable, but might be interesting. ; ; Thanks to F. Slijkerman for some tweaks. ; Thanks to Linas Vepstas for the math. ; ; Written by Damien M. Jones ; init: complex il = 1/log(@power) ; Inverse log (power). float lp = log(log(@bailout)) ; log(log bailout). final: #index = 0.05 * real(#numiter + il*lp - il*log(log(cabs(#z)))) default: title = "Smooth (Mandelbrot)" helpfile = "Uf*.chm" helptopic = "Html/coloring/standard/smooth.html" $IFDEF VER50 rating = recommended $ENDIF 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 usually 2." endparam param bailout caption = "Bail-out value" default = 128.0 min = 1 hint = "This should be set to match the bail-out value in \ the Formula tab. This formula works best with bail-out \ values higher than 100." endparam }

### binary decomposition[edit]

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. } BinaryDecomposition { ; from standard.ucl ; Classic binary decomposition. Can give quite abstract effects. ; Use low bail-out values in the fractal formula (if possible) for ; best effects. This coloring algorithm uses just two colors from ; the gradient: one from the left end and one from the middle. ; final: if @type == "Type 1" if real(#z) * imag(#z) >= 0 #index = 0.5 else #index = 0 endif else if atan2(#z) > 0 #index = 0.5 else #index = 0 endif endif default: title = "Binary Decomposition" helpfile = "Uf3.chm" helptopic = "Html/coloring/standard/binarydecomposition.html" param type caption = "Decomposition Type" enum = "Type 1" "Type 2" default = 0 hint = "Toggles between two types of binary decomposition. Type 2 \ reproduces the coloring used with many images in the classic \ Beauty of Fractals book." endparam }

### slope[edit]

// http://www.fractalforums.com/mandel-machine/maybe-perturbation-could-go-with-a-slope/ mbrot2_slope { fractal: title="mbrot2_slope" width=1024 height=400 layers=1 credits="Alef;12/4/2014;Frederik;7/23/2010" layer: caption="Background" opacity=100 mapping: center=-0.61777095064903/0.6790465094562 magn=19180.711 angle=156.5545 formula: maxiter=1000 filename="Standard.ufm" entry="SlopeMandel" p_start=0/0 p_power=2/0 p_bailout=1.0E20 p_offset=0.000000000000001 p_zmode=potential p_xfer=linear p_zscale=1.0 p_zscale2=0.005 p_everyiter=no inside: transfer=none outside: transfer=linear filename="Standard.ucl" entry="Decomposition" gradient: comments="slightly changed standart. IMHO good sky." smooth=no rotation=1 index=0 color=6303744 index=64 color=12085789 index=168 color=16777197 index=257 color=33023 index=343 color=512 opacity: smooth=no index=0 opacity=255 } mbrot3_slope { ; copyright Kerry Mitchell 15sep98 ; ; sample image to illustrate ; embossing effect fractal: title="mbrot3_slope" width=1024 height=512 layers=1 credits="Alef;12/4/2014;Kerry Mitchell;9/15/1998" layer: caption="Layer 1" opacity=100 method=linear mapping: center=-0.81810721128409/0.19884197484006 magn=4118.0018 angle=34.1619 formula: maxiter=1000 percheck=off filename="Standard.ufm" entry="SlopeMandel" p_start=0/0 p_power=2/0 p_bailout=1.0E20 p_offset=0.000000000000001 p_zmode="distance estimator" p_xfer=linear p_zscale=1.0 p_zscale2=0.005 p_everyiter=no inside: transfer=none outside: transfer=linear filename="Standard.ucl" entry="Decomposition" gradient: comments="slightly changed standart. IMHO good sky." smooth=no rotation=1 index=0 color=6303744 index=64 color=12085789 index=168 color=16777197 index=257 color=33023 index=343 color=512 opacity: smooth=no index=0 opacity=255 }

### field lines[edit]

"There's a later version of my formula for field lines - though somewhat extended to include smooth iteration, distance estimation and distance estimation angles in my class formulas for UF - mmf.ulb called "MMF Field Estimator" It's a UF class formula so not quite so easy to follow but I think it should be clear enough. I boiled down "corrections" to field lines that work in most places but at the moment require manual adjustment to work properly - these are the two parameters that can be modified by the user to fix errors in the field lines, unfortunately you can't always fix them everywhere in view even then but this is about as close as you can get I think. I tried including the MMF Field Lines code here but unfortunately it's too long, it's in mmf.ulb in te Ultra Fractal Formula database at: http://formulas.ultrafractal.com/ " David Makin

MMF3-FieldLines { ; ; This version of calculating field lines will work reasonably well with both ; Mandelbrot and Julia Sets for divergent fractals with a divergence that is ; close to being a positive integer >=2 but can also produce quite interesting ; results with fractals that do not fit that criteria - just not rendering the ; field lines correctly in other cases :-) ; ; Thanks to Chris Hayton for showing me how to fix the "off-by-one" problems. ; http://www.fractalforums.com/programming/smooth-external-angle-of-mandelbrot-set/ ; David Makin ; Here's my code from mmf3.ucl for Ultra Fractal: ; global: float twopi = 2.0*#pi float dtwopi = 0.5/#pi float dp = 1.0/@power float m = @power*dtwopi float dp2 = 1.0/(2.0+@power) ; Changed from originally trying 1/power init: complex zv[#maxiter] int i = 0 float a = 0.0 float b = 0.0 float c = 0.0 float s = 0.0 if @julia zv[i] = #z i = i + 1 endif loop: zv[i] = #z i = i + 1 final: if (s = atan2(#z))<0 s = s + twopi endif while i > @skipiter i = i - 1 if @version==0 b = (@power*atan2(zv[i]))%twopi else b = atan2(zv[i]^@power) endif if b < 0.0 b = b + twopi endif c = c + b - s if c >= #pi s = s + twopi if @fixit || @accident c = c - twopi endif elseif c < -#pi s = s - twopi if @fixit || @accident c = c + twopi endif endif if @fixit c = dp2*c elseif !@accident c = 0.0 endif if (a = atan2(zv[i])) < 0.0 a = a + twopi endif s = dp*(s + twopi*floor(a*m)) endwhile s = s*dtwopi if @fixskip while s<0.0 s = s + 1.0 endwhile while s>=1.0 s = s - 1.0 endwhile endif #index = s default: title = "MMF3 Field Lines (use high bailouts)" heading caption = "Information" ; text = "This colouring is a little touchy around certain values, if you \ ; get obvious lines or dots that shouldn't be there but the 'Degree \ ; of Divergence' is set properly for the main formula and you are \ ; using a high bailout of say 1e20 or higher then try \ ; adjusting the location very slightly. For example if vertical \ ; lines appear on an unrotated fractal then try changing the x \ ; (real) location very slightly, if horizontal lines appear then try \ ; changing the y (imag) location very slightly." endheading heading endheading param version caption = "Version" enum = "Original" "Alternative" default = 1 hint = "Allows you to modify one of the calculations in the formula that \ is particularly sensitive to small errors. Ideally both methods \ should produce identical results but they don't, so if you get \ visible errors using one method then try the other (assuming you \ have the divergence set correctly and are using a high bailout)." endparam param power caption = "Degree of divergence" default = 2.0 hint = "This is an estimate of the divergence of the main formula, e.g. 2 \ for z^2+c, 3 for z^3+c etc." endparam param julia caption = "Julia ?" default = false hint = "Enable for correct rendering of Julia Sets." endparam param skipiter caption = "'Start' iteration" default = 0 min = 0 hint = "You can use this to attempt to get better detail at higher \ iteration depths, note that it only works as intended with 'Color \ Density' as a whole integer >=1." endparam param fixskip caption = "Fix 'Start' iteration" default = false hint = "Fixes a problem when the start iteration is non-zero and maybe in \ other cases - specifically if you get solid areas of palette \ colour zero when the Transfer Function is Linear this may fix the \ problem." endparam param fixit caption = "Fix Field Lines" default = false hint = "Enable this to make the formula much more accurate at rendering \ the field lines correctly. It's a fudge produced after trial and \ error but is quite effective at correcting some areas." endparam param accident caption = "Happy Accident" default = false hint = "You may find the colouring useful when this is enabled. This \ is available as I found the results when initially adding the \ 'Fix it' option quite interesting." visible = !@fixit endparam }

# images[edit]

# files[edit]

- ufr : Fractal Files *.ufr
- upr : Displays parameter files (*.upr)
- par : Older Fractint parameter files (*.par)
- ugr : Displays gradient files (*.ugr)
- ual : Older gradient files (*.ual)
- map : Fractint palette files (*.map)
- uxf : Displays transformation files (*.uxf)
- ufm : Displays fractal formula files (*.ufm). Fractal formula files contain multiple fractal formulas. Older Fractint formula files (*.frm) are also shown. See Fractal formulas.
- ucl : Displays coloring algorithm files (*.ucl). See also writing coloring algorithm
- ulb : Displays plug-in library files (*.ulb)

# gradient[edit]

- stackoverflow question: which-color-gradient-is-used-to-color-mandelbrot-in-wikipedia
- Ultra Fractal Tutorial: Create a New Gradient File