Martsam Formulas
From Ultrafractal Wiki
The Martsam Formulas are a set of Fractal Formulas in sam.ufm.
What is it?
These formulas are inspired by the Martin formula by Mark Townsend. They perform transformations on the real and the imaginary part of z. There is no bailout, so the iterations are performed "maxiter" times and all the points are inside. You have to load an inside colouring. The best coloring is imho "Magnitude" in mt.ucl. Orbit traps, Lyapunov, Gaussian Integer and the various fBm colorings usually work well, too.
Parameters
These formulas need four real parameters. These parameters are the real and imaginary parts of "a" and "b". The bigger a and b are, the more complex the shapes displayed are. If you enable the the "|a| = |b| = c ?" feature, the modulus of a and b (their "size") will be equal to c. So you can enable this feature, modify c until the shapes are complex enough, and then modify a and b to get other patterns of the same complexity. Usually, increasing the Maximum Iterations will also increase the pattern complexity.
The "Mode" parameter describes an additional term added each iteration. x and y are the current real and imaginary parts of z and x1 and y1 are the real and imaginary parts of the first value of z (the pixel).
The real func 1 is applied to x1 and the imaginary func 1 is applied to y1.
Examples
Copyright 1999 Samuel Monnier
msgn1 {
; Copyrights 1999 S. Monnier
; http://www.crosswinds.net/~s31415/index/index.htm
; framing changed slightly by JP
fractal:
title="msgn1" width=600 height=600 author="Samuel"
created="November 7, 1999" numlayers=4
layer:
caption="New Layer 3" opacity=66 visible=yes alpha=no mergemode=overlay
mapping:
center=3.61075077699414336/-0.837886506605109504
magn=0.476190621563212608 angle=199.785907368287008
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1.4 p_ab1=yes f_fr1=ident
f_fi1=ident
inside:
filename="mt.ucl" entry="mt-soft-gnarly" density=0.1 transfer=arctan
repeat=yes p_formula="Vine" p_flav="0" p_spread=1 p_points=8 p_center=no
p_a=3 p_b=2 p_iters=20 p_flavor=3 p_h=0.03 p_offset=0/0 p_scale=0.4
p_p_scale=1 p_link=yes f_pn1=atanh f_tn1=ident f_tn2=ident f_tn3=ident
f_gn1=sin f_gn2=tan f_gn3=cos
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=3 index=20 color=0 index=93 color=14935011 index=287
color=0
layer:
caption="New Layer 2" opacity=100 visible=yes alpha=no mergemode=overlay
mapping:
center=3.61075077699414336/-0.837886506605109504
magn=0.476190621563212608 angle=199.785907368287008
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1.4 p_ab1=yes f_fr1=ident
f_fi1=ident
inside:
filename="mt.ucl" entry="mt-soft-gnarly" density=0.1 transfer=arctan
repeat=yes p_formula="Vine" p_flav="0" p_spread=1 p_points=8 p_center=no
p_a=3 p_b=2 p_iters=20 p_flavor=3 p_h=0.03 p_offset=0/0 p_scale=0.4
p_p_scale=1 p_link=yes f_pn1=ident f_tn1=ident f_tn2=ident f_tn3=ident
f_gn1=sin f_gn2=tan f_gn3=cos
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=4 index=3 color=0 index=23 color=5794186 index=37
color=10263708 index=63 color=1383472
layer:
caption="Layer 1" opacity=75 visible=yes alpha=no mergemode=softlight
mapping:
center=3.61075077699414336/-0.837886506605109504
magn=0.476190621563212608 angle=199.785907368287008
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1.4 p_ab1=yes f_fr1=ident
f_fi1=ident
inside:
filename="mt.ucl" entry="mt-soft-gnarly" density=0.1 transfer=arctan
repeat=yes p_formula="Popcorn" p_flav="0" p_spread=1 p_points=8
p_center=no p_a=3 p_b=2 p_iters=20 p_flavor=2 p_h=0.02 p_offset=0/0
p_scale=1 p_p_scale=1 p_link=no f_pn1=ident f_tn1=ident f_tn2=ident
f_tn3=ident f_gn1=sin f_gn2=tan f_gn3=cos
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=3 index=0 color=0 index=32 color=10263708 index=58
color=3692900
layer:
caption="New Layer 1" opacity=38 visible=yes alpha=no mergemode=multiply
mapping:
center=3.61075077699414336/-0.837886506605109504
magn=0.476190621563212608 angle=199.785907368287008
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1.4 p_ab1=yes f_fr1=ident
f_fi1=ident
inside:
filename="mt.ucl" entry="mt-soft-gnarly" density=0.1 transfer=arctan
repeat=yes p_formula="Vine" p_flav="0" p_spread=1 p_points=8 p_center=no
p_a=3 p_b=2 p_iters=20 p_flavor=2 p_h=0.05 p_offset=0/0 p_scale=1
p_p_scale=1 p_link=yes f_pn1=ident f_tn1=ident f_tn2=ident f_tn3=ident
f_gn1=sin f_gn2=tan f_gn3=cos
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=2 index=19 color=0 index=98 color=12768475
}
Copyright 1999 Samuel Monnier
Martsamexpl1 {
; Copyrights 1999 S. Monnier
; http://www.crosswinds.net/~s31415/index/index.htm
fractal:
title="Martsamexpl1" width=600 height=600 author="Samuel"
created="August 7, 1999" numlayers=4
layer:
caption="New Layer 3" opacity=100 visible=yes alpha=no mergemode=overlay
mapping:
center=0.751725924741347055/2.35425305339143198 magn=0.810582606248240923
angle=44.2151647052804267
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1 p_ab1=no f_fr1=ident f_fi1=ident
inside:
filename="lkm.ucl" entry="gauss" transfer=linear repeat=yes
p_inttype="round(z)" p_colorby="maximum distance" p_norm="none" p_fac=2/1
outside:
transfer=linear repeat=yes
gradient:
smooth=no position=103 numnodes=2 index=103 color=3684408 index=303
color=16777215
layer:
caption="New Layer 2" opacity=100 visible=yes alpha=no mergemode=overlay
mapping:
center=0.751725924741347055/2.35425305339143198 magn=0.810582606248240923
angle=44.2151647052804267
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1 p_ab1=no f_fr1=ident f_fi1=ident
inside:
filename="lkm.ucl" entry="gauss" transfer=linear repeat=yes
p_inttype="round(z)" p_colorby="minimum distance" p_norm="none" p_fac=2/1
outside:
transfer=linear repeat=yes
gradient:
smooth=no position=103 numnodes=2 index=102 color=2434378 index=304
color=12182271
layer:
caption="New Layer 1" opacity=100 visible=yes alpha=no mergemode=overlay
mapping:
center=0.751725924741347055/2.35425305339143198 magn=0.810582606248240923
angle=44.2151647052804267
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1 p_ab1=no f_fr1=ident f_fi1=ident
inside:
filename="dmj.ucl" entry="dmj-Triangle" transfer=linear repeat=yes
p_apower=1 p_aflavor="normal" p_power=2 p_bailout=1E20
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=2 index=0 color=0 index=202 color=8503551
layer:
caption="Layer 1" visible=yes alpha=no
mapping:
center=0.751725924741347055/2.35425305339143198 magn=0.810582606248240923
angle=44.2151647052804267
formula:
filename="sam.ufm" entry="MartSam1" maxiter=5 percheck=normal
p_mode="x1 ; y1" p_a=1/-1 p_b=1/1 p_c=1 p_ab1=no f_fr1=ident f_fi1=ident
inside:
filename="dmj.ucl" entry="dmj-CarlsonAtan2" transfer=linear repeat=yes
outside:
transfer=linear repeat=yes
gradient:
smooth=no numnodes=2 index=0 color=71748 index=200 color=11263231
}
