Below are:
1) Albrecht's instructions -- long version -- for how to use
his multifractal_10 (MFR-10) formula, and
2) The multifractal_10 formula with all the comments stripped
out, (from Albrecht's latest post) -- in hopes of being able
to run it in DOS Fractint.
Notes:
1) I have not yet run the multifractal_10 less comments below.
I plan to give it a try -- I was unsuccessful when
attempting to use the version *with* comments in April
of 2011 -- I got DOS Fractint errors.
2) You'll need to choose one of Albrecht's parameter sets
that he's recently posted to use with the comment-less
formula below.
- Hal Lane
########################
# hallane(a)earthlink.net
########################
Albrecht's Instructions on How to Use Multifractal_10
-----------------------------------------------------
;A few words though about multifractal_10.
;It is the final version, it handles 8 basic fractal
;formulas and combines ANY 5 to one multifractal image.
;(1) Secant (Mike Wareman)
;(2) Mandel (Special version Puskas Istvan)
;(3) Bees (Ray Girvan)
;(4) Julia (Special version Puskas Istvan)
;(5) Many mods (Linda Allison)
;(6) Phoenix (Mike Wareman)
;(7) Newton (Special Version Puskas Istvan)
;(8) Spiderjul (John Horner).
;An easy tweak is real(p2) (Z-screen), just list 5 numbers
;of above list in front of the dot. Multiple entries of the
;same number or any other combinations are possible.
;To get the basic image just use one number followed by 4
;zeros. The sequence of the five numbers defines following:
;Shape - outside - inside1 - inside2 - inside3.
;To activate S.Gallet´s "Lake Effect" type "1" in front
;the dot image(p5) and after the dot 6 digits as stated below.
;I did some exploring and testing, did not detect any fractint
;error. Exploring cant be complete. there are far too many
;possibilities, found that any combination delivered an image
;ready to zoom into.
;
; Multifractal_10 composes images using max 5 different formulas
; simultaneously. There are 9 frms to choose from. There are five
; "channels": basic shape, outside and inside 1-3.The transitions
; are controlled by an iteration counter or by border (z) values,
; in and out (bigger or smaller), or iteration and border
; simultaneously.
;
; At the transition points optional resets are provided, either of the
; iteration counter or the z-value (or both), which affect the coloring
; and further iteration.
;
; Five different bailout values can be applied, ranging from 1 to
; one million. The effect is compression or expansion of the colours.
;
; A unique programmable "warp-effect" can be applied to each channel.
; It changes the behaviour and looks of the channels, pending on
; previous iterations, a choosable function and a "warp" factor. Maybe
; this just means a distortion, maybe a 3d effect.
;
; Sylvie Gallet's lake effect is optional, fully integrated and
; works with all formulas, inside3 is shut off if activated.
;
; There now is a second basic "Double mandel" which allows the creation
; of "mandscapes", 2 samples with different insides, symmetric or
; asymmetric are provided.
;
;
; "Debugflag=322" must be deactivated. Please check your SS-tools.ini.
;
; Multifractal_10 Inputs:
;
; Real P2
; First Input (before the dot)
; 5 Digits : Channels : 1_Basic Shape 2_Outside 3_Inside1 4_Inside2
5_Inside3
; Frms: 1_Secant 2_Mandel(2) 3_Bees 4_Julia 5_Many Mods 6_Phoenix 7_Newton
8_Spider
; Second Input (after the dot)
; 2 Digits_Many Mods_Number of sides 2 Digits_Phoenix 2 Digits_Spider
; 1 Digit_Reset on Transitions (Shape) 0_no 1_Dble Mandel 2_Iter-reset
3_both +5_warp
; 4 Digits_Reset Channels 2-5 0_no 1_z-reset 2_Iter-reset 3_both +5_warp
;
; Imag P2
; First Input
; 5 Digits_Colour (Bailout) Number for each channel (5 available)
; Second Input
; Variables : 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees
;
; Real P3
; First Input
; 2 Digits_Newtonvariable 4 Digits_Colour1
; Second Input
; 5 Digits_Colour2 5 Digits_Colour3
;
; Imag P3
; First Input
; Basic Shape : Warp-factor (fn1 is used)
; Second Input
; 5 Digits_Colour4 6 Digits_Colour5
;
; Real P4
; First Input
; Outside : Warp-factor (fn2 is used)
; Second Input
; Outside : 4 Digits+1fractal digit_Border-out 4 Digits+1
fractaldigit_Border-in
;
; Imag P4
; First Input
; Inside1_Maxiter
; Second Input
; Inside1 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin
+5_maxiter+border
; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1
;
; Real P5
; First Input
; Inside2_Maxiter
; Second Input
; Inside2 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin
+5_maxiter+border
; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2
;
; Imag P5
; First Input
; Inside3_Maxiter
; Second Input
; Inside3 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin
+5_maxiter+border
; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractal digit_border3
; Alternate Input Imag P5
; First Input : 1_Lake effect enabled (Inside3 disabled)
; Second Input : 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude
;
;
; Inputs Multifractal_10:
;
;p1 (spider)julia-seed
;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3
;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider
; input2: 2digits_many-mods 2digits_phoenix 2digits_spider
; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp
; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp
;imag(p2)(-) 5digits_colour(bailout) number
; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees
;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3
;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5
;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in
;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in
; 5digits_factor1 (fn2) 4digits+fract_border1
;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in
; 5digits_factor2 (fn3) 4digits+fract_border2
;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in
; 5digits_factor3 (fn4) 4digits+fract_border3
; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl
;fn(1) shared by many-mods+bees
;
===========================================================================
===========================================================================
Multifractal_10 Less Comments
-----------------------------
========= Beginning of Formula ============================================
frm:Multifractal_10 {
le=0
z=pixel
da=real(p2)
dd=trunc(da)
da=round((da-dd)*100000000000)+11111
dd=dd+11111
d=trunc(dd/10000)
dd=dd-d*10000
d3=(d==4)+(d==5)+(d==8)+(d==9)
d4=d3==0
vb=d>5
sc=d==2
mo=d==6
px=d==7
ab=px+(d==3)+(d==5)+(d==9)
d=trunc(dd/1000)
dd=dd-d*1000
ex1=d>1
sc1=d==2
mo1=d==6
px1=d==7
v1m=mo1+px1
v1j=d>7
dd1=v1j+(d==4)+(d==5)
ab1=px1+(d==3)+(d==5)+(d==9)
d=trunc(dd/100)
dd=dd-d*100
ex2=d>1
sc2=d==2
mo2=d==6
px2=d==7
v2m=mo2+px2
v2j=d>7
dd2=v2j+(d==4)+(d==5)
ab2=px2+(d==3)+(d==5)+(d==9)
d=trunc(dd/10)
ex3=d>1
sc3=d==2
mo3=d==6
px3=d==7
v3m=mo3+px3
v3j=d>7
dd3=v3j+(d==4)+(d==5)
ab3=px3+(d==3)+(d==5)+(d==9)
d=dd-d*10
ba=imag(p5)
mi3=trunc(ba)
dd=(d>1)+(mi3>1)
ex4=dd==2
sc4=d==2
mo4=d==6
px4=d==7
v4m=mo4+px4
v4j=d>7
dd4=v4j+(d==4)+(d==5)
ab4=px4+(d==3)+(d==5)+(d==9)
mm=trunc(da/1000000000)
da=da-mm*1000000000
ph=trunc(da/10000000)/100
da=da-ph*1000000000
sp=trunc(da/100000)/100
da=da-sp*10000000
d=trunc(da/10000)
ex0=d>4
da=da-d*10000
d=d-5*ex0
dm=(d==2)+(d==4)
ir0=(d==3)+(d==4)
d=trunc(da/1000)
w1=d>4
da=da-d*1000
d=d-5*w1
rs1=(d==2)+(d==4)
ir1=(d==3)+(d==4)
d=trunc(da/100)
w2=d>4
da=da-d*100
d=d-5*w2
rs2=(d==2)+(d==4)
ir2=(d==3)+(d==4)
d=trunc(da/10)
w3=d>4
da=da-d*10
d=d-5*w3
rs3=(d==2)+(d==4)
ir3=(d==3)+(d==4)
d=round(da)
w4=d>4
d=d-5*w4
rs4=(d==2)+(d==4)
tt=ex1+ex0+ex2+ex3+ex4
d=real(p3)
dd=trunc(d)
da=(d-dd)*10000000000
pp=trunc(dd/10000)
ba1=dd-10000*pp
ba2=trunc(da/100000)
ba3=da-100000*ba2
d=imag(p3)
sfac=trunc(d)
da=(d-sfac)*100000000000
ba4=trunc(da/1000000)
ba5=da-ba4*1000000
d=real(p4)
ofac=trunc(d)
da=(d-ofac)*10000000000
bh=trunc(da/100000)/10
bl=(da-bh*1000000)/10
bs=bl/2
d=imag(p2)
t=d<0
if (t)
d=-d
endif
dd=trunc(d)
da=round((d-dd)*10000000000)
d=trunc(dd/10000)
dd=dd-d*10000
bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/1000)
dd=dd-d*1000
bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/100)
dd=dd-d*100
bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/10)
dd=dd-d*10
bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=round(dd)
bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=da
p0=trunc(d/100000000)/10
d=d-p0*1000000000
p6=trunc(d/1000000)/10
d=d-p6*10000000
if (t)
p6=-p6
endif
p7=trunc(d/10000)/10
d=d-p7*100000
dp=p6+p0/100
p8=trunc(d/100)/100
d=d-p8*10000
p9=d/100
d=imag(p4)
mi1=trunc(d)
da=(d-mi1)*100000000000
d=trunc(da/10000000000)
bt1=d>6
da=da-d*10000000000
d=d-5*bt1
dt1=d>1
iv1=d==3
fac1=trunc(da/100000)
da=da-fac1*100000
bo1=(da/100000)/10
d=real(p5)
mi2=trunc(d)
da=(d-mi2)*100000000000
d=trunc(da/10000000000)
bt2=d>6
da=da-d*10000000000
d=d-5*bt2
dt2=d>1
iv2=d==3
fac2=trunc(da/100000)
da=da-fac2*100000
bo2=(da/100000)/10
if (mi3==1)
d=(ba-mi3)*1000000
fr=round((trunc(d/10000))*10)
d=d-fr*1000
lv=(trunc(d/100))/100
d=d-lv*10000
am=d/100
u=real(rotskew*pi/180)
t=exp(-flip(u))
bo=1/real(magxmag)
q=bo/0.75*imag(magxmag)
dd=tan(imag(rotskew*pi/180))
da=2*q*t
rs=2*bo*(dd+flip(1))*t
zz=center+(-q-bo*dd-flip(bo))*t
z=z-zz
d=imag(conj(da)*z)/imag(conj(da)*rs)
le=d<=lv
if (le)
dd=lv-d
z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs
endif
z=z+zz
else
da=(ba-mi3)*100000000000
d=trunc(da/10000000000)
bt3=d>6
da=da-d*10000000000
d=d-5*bt3
dt3=d>1
iv3=d==3
fac3=trunc(da/100000)
da=da-fac3*100000
bo3=(da/100000)/10
endif
if (vb)
if (d3)
if (ab)
z=z*le+pixel*(le==0)
c=p1
else
z=z*le+pixel*(le==0)
c=p1
endif
elseif (ab)
c=z
z=z*le+pixel*(le==0)
else
c=0.4*log(sqr(z^mm))
z=0
endif
elseif (d3)
if (ab)
c=p1
z=z*le+pixel*(le==0)
else
c=p1
z=z*le+pixel*(le==0)
endif
elseif (ab)
c=z
z=0
else
c=z
z=z*le+pixel*(le==0)
endif
t=0
bo=|z|
p=pp
z0=p7
zold=(0.0,0.0)
cb=p9
ba=bb0
:
if (tt)
t=t+1
if (ex0)
ex0=t<mi1
if (bo>bs)
u=2*(fn1(t/sfac))
ex0=0
if (ir0)
t=0
endif
if (d4)
z=z*u
if (mo)
c=0.4*log(sqr(z^mm))
else
c=pixel
endif
else
z=z*le+pixel*(le==0)
cb=p9*u
c=p1*u
p=pp*u
endif
tt=tt-1+ex0
endif
elseif ((ex1)&&bo>bl)
if (bo<bh)
d3=dd1
ba=bb1
ab=ab1
ex1=0
tt=tt-1
if (w1)
u=2*(fn2(t/ofac))
else
u=1,0
endif
if (ir1)
t=0
endif
if (d3)
vb=v1j
if (rs1)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
c=p1
z=z*u
cb=p9
endif
else
vb=v1m
if (rs1)
c=z*u
z=pixel*(sc1+px1)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo1)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex2)
if (dt1)
if (iv1)
d=bo>bo1
else
d=bo<bo1
endif
if (bt1)
d=d+(t>mi1)
endif
else
d=t>mi1
endif
if (d)
ab=ab2
d3=dd2
ba=bb2
ex2=0
tt=tt-1
if (w2)
u=2*(fn2(t/fac1))
else
u=1,0
endif
if (ir2)
t=0
endif
if (d3)
vb=v2j
if (rs2)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v2m
if (rs2)
c=z*u
z=pixel*(sc2+px2)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo2)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex3)
if (dt2)
if (iv2)
d=bo>bo2
else
d=bo<bo2
endif
if (bt2)
d=d+(t>mi2)
endif
else
d=t>mi2
endif
if (d)
ab=ab3
d3=dd3
ba=bb3
ex3=0
tt=tt-1
if (w3)
u=2*(fn3(t/fac2))
else
u=1,0
endif
if (ir3)
t=0
endif
if (d3)
vb=v3j
if (rs3)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v3m
if (rs3)
c=z*u
z=pixel*(sc3+px3)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
vb=v3m
if (mo3)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex4)
if (dt3)
if (iv3)
d=bo>bo3
else
d=bo<bo3
endif
if (bt3)
d=d+(t>mi3)
endif
else
d=t>mi3
endif
if (d)
ab=ab4
d3=dd4
ba=bb4
ex4=0
tt=0
if (w4)
u=2*(fn4(t/fac3))
else
u=1,0
endif
if (d3)
vb=v4j
if (rs4)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v4m
if (rs4)
c=z*u
z=pixel*(sc4+px4)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo4)
c=0.4*log(sqr(z^mm))
endif
endif
endif
endif
endif
if (vb)
if (d3)
if (ab)
z=z*z+c
c=c*sp+z
else
z1=z^p-1
z2=p*z*z
z=z-z1/z2
endif
elseif (ab)
z1=z*z+0.56+ph/100-0.5*zold
zold=z
z=z1
else
z2=fn1(z)+c
z1=cos(z2)
z=c*(1-z1)/(1+z1)
endif
elseif (d3)
if (ab)
z2=z*z
z=z2*z2+p6*z2+c-p0
else
z1=fn1(z)-cb
z2=z1^p8-1
z3=p8*(z1^(p8-1))
z=z-(z2/z3)
endif
elseif (ab)
if (dm)
z=z*z+c+c*c-dp
else
z2=z*z
z=z2*z2+p6*z2+c-p0
endif
else
z3=z
z1=z0*z0*z0*z0-1
z2=z*z*z*z-1
z=z-z2*(z-z0)/(z2-z1)
z0=z3
endif
bo=|z|
bo<ba
}
========= End of Formula ===================================
