Hi,
a lot of changes and new options this time.
1. All channels now have an own input, which is referred to by name,
no shared inputs anymore. This means all formulas can be tested without
doing any changes except imag(p2) as explained. Use the second input
to alternately use an (almost) basic mandel (channel1) or julia (channel2)
instead of the default frms. If you want to test a formula exclusively,
just type the number followed by four zeros as first input.
2. Just add 5 to the secondary inputs after the 2digits many_mods input
to activate the warp-effect separetely for each channel. This is useful in
many instances f.e. to change the looks of the inside/outside images and
to preserve the julia settings. Add 5 to the primary inputs to do a reset
for each channel. This causes that the in/outside image is adjusted to
the screen instead of the surroundings. This also works if the warp-effect
is shut off, test it.
3. For simplicity reasons "ismand" is not used anymore, so one more line
of the text is displayed and the inputs are not ambivalent anymore.
4. A new mixing formula "Secant" is available as default channel one.
Check the first par to see what it looks like.
In order to go on with this I need some feedback, so I know what Iïm
doing this for. So please post your images and your comments. I regard this
as a "living" process on the way to perfection, I still have some ideas
and critics should help to improve it.
Dont hesitate to play around with multifractal, if youïre interested.
Youïll see that itïs fun and quite easy once the basics are understood.
An easy tweak is to use other functions, fn1 if bees or many_mods is used,
the other ones to affect the warp effects. Cosxx will create weird
effects in many cases.
Fractal greetings,
Al.
----------------------------start-par-------------------------------------
Mandelbug { ; Albrecht Niekamp July, 03
; Outside secant inside newton\bees\julia
; Time 0.18.47.56
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/cos passes=t
center-mag=0.420263/4.44089e-016/1.718213/1/-90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/11972.3215501/5040.060802\
1613/4084.02048/384.000004/768.00024/128.00768/384.00768/768.00768000000\
01 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4
periodicity=0 rseed=-2436
colors=200000<3>764985BA6DC7FE8<17>niQpjRrlS<3>ysX<25>BB7996775<3>000<24\
>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss\
<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<30>022
}
---------------------------------end---------------------------------------
Gran_canyon { ; inside mandel,mandel,julia
; Albrecht Niekamp July, 03
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t
center-mag=1.10912/0.314452/26.9208/1/-90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\
1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\
1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis
logmap=old periodicity=0 rseed=-2436
colors=200200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677\
455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>\
ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<29>400
}
Gran_canyon_zoom { ; Albrecht Niekamp July, 03
; Time 0.20.10.67
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t
center-mag=+1.14003818818291000/+0.35936443447906610/197.9471/1/-90/3.88\
578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\
1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\
1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis
logmap=old periodicity=0 rseed=-2436
colors=200N00<6>900<3>200000122<5>BCCDEEFGGGHHIJJKLL<13>hiijkkkll<3>rss<\
21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>0220001\
11<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<18>\
P00
}
Bishops_hat { ; Albrecht Niekamp July, 03
; Time 0.33.58.01
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=exp/sin/exp/sin passes=t
center-mag=0.431817/2.22045e-016/1.34604/1/-90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/10112.3210611/2543.060802\
1613/4084.02048/384.0000076/768.00024/128.0076800000001/512.007680000000\
1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis
logmap=6 periodicity=0 rseed=-2436
colors=200700<3>000<5>9AABCCDEEFGGGHH<15>hiijkkkll<3>rss<21>HIIFGGEFF<3>\
677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQ\
pjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<26>900
}
Magic_circle_2 { ; Albrecht Niekamp July, 03
; Time 0.10.55.37
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/exp passes=t
center-mag=2.22045e-016/-2.22045e-016/0.8392416/1/90/3.88578058618804789\
e-016
params=0.8202154606769005/-0.06207464827417833/40673.3255005/25040.06080\
21613/2048.02048/768.0000045/768.00024/128.0076800000001/512.00768000000\
01/768.0076800000001 float=y maxiter=2048 inside=maxiter
outside=tdis logmap=old periodicity=0 rseed=-2436
colors=200JHA<13>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r0\
0<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFG\
GEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<7>HF9
}
Universal_robot { ; Time 0.34.13.72
; Albrecht Niekamp July,03
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/sin passes=t
center-mag=-0.0124931/3.747e-016/11.03753/1/-90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/14178.321055/2540.0608021\
613/4084.02048/384.0000045/768.00024/128.0076800000001/256.0076800000001\
/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis
logmap=3 periodicity=0 rseed=-2436
colors=200554<2>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABB\
BCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz\
<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<27>775
}
Mandelmania_zoom { ; makes the 4th generation mandel visible
; Albrecht Niekamp July,03
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t
center-mag=+0.84947498866192170/+0.00000000000000022/895.0965/1/180
params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\
1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\
1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis
periodicity=0 rseed=-2436
colors=200b00<6>p00<3>w00y00w00<24>C00A00800<3>000<2>455677899ABBBCC<18>\
hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C\
08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<17>`00
}
Mandeline { ; most unsual musical instrument
; Albrecht Niekamp July,03
; Mandelmania deepzoom, takes a while
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t
center-mag=+0.84820315604180700/+0.00000000000000022/29638.96/1/-90/3.88\
578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\
1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\
1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis
periodicity=0 rseed=-2436
colors=200C00<4>200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF\
<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjR\
rlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<24>E00
}
The_big_bed { ; Time 0.29.40.30
; Albrecht Niekamp July,03
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/sin passes=t
center-mag=-0.0108791/3.46945e-016/16.7049/1/90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/14182.3215551/5040.060802\
1613/4084.02048/384.0000045/768.00024/128.0076800000001/384.00768/768.00\
76800000001 float=y maxiter=2048 inside=maxiter outside=tdis
logmap=3 periodicity=0 rseed=-2436
colors=2000Wd<14>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB\
7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18\
>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<9>0Xf
}
Mandelmania_2 { ; Time 0.16.49.48
; Albrecht Niekamp July,03
; Version 2002 Patchlevel 5
reset=2002 type=formula formulafile=mult244.frm
formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t
center-mag=0.47425/2.22045e-016/1.249125/1/-90/3.88578058618804789e-016
params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\
1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\
1/512.00746 float=y maxiter=4084 inside=maxiter outside=tdis
logmap=yes periodicity=0 rseed=-2436
colors=200VVV<7>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2>\
0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000\
400<23>o00q00s00<3>z00<25>C00A00800<3>000<16>UUU
}
------------------------------------------start-frm-----------------------
FRM:Multifractal_6 { ; Albrecht Niekamp 020703
;only integers as first input, second input 5 digits to the right
;real(p2) 5digits: shape, outside, in1, in2, in3
; 0_off 1_secant/mand 2_bees/jul 3_m_mods 4_newt +5_reset (not shape)
; input2 : 2digits_m_mods 5digits_mand/jul use : 0_no 1_yes +5_warp
;imag(p2)(-) 2-4digits : quasinewton input (max 2000)
; 1digit : no m_mods multipl. : 1_out 2_in1 3_in2 4_all
; 1digit : iter-reset 1_out 2_in1 3_in2 4_all
; input2 : 4digits(-)_mand 2digits_secant 4digits_bees
;real(p3) many_mods bailout, bailout
;imag(p3) shape : factor (fn1), outside : border-in
;real(p4) outside : factor (fn2), border-out
;imag(p4) inside1 : maxiter1, factor1 (fn2)
;real(p5) inside2 : maxiter2, factor2 (fn3)
;imag(p5) inside3 : maxiter3, factor3 (fn4)
;fn(1) is shared by bees and many_mods
;
da=real(p2)
dd=trunc(da)
da=round((da-dd)*10000000)+11111
d=trunc(dd/10000)
t=d>5
dd=dd-d*10000
d=d-5*t
d3=(d==2)+(d==4)
d4=(d3==0)
vb=(d==3)+(d==4)
d=trunc(dd/1000)
ex1=d>0
dd=dd-d*1000
rs1=d>5
d=d-5*rs1
v1m=(d==3)
v1j=(d==4)
dd1=(d==2)+(d==4)
d=trunc(dd/100)
ex2=d>0
dd=dd-d*100
rs2=d>5
d=d-5*rs2
v2m=(d==3)
v2j=(d==4)
dd2=(d==2)+(d==4)
d=trunc(dd/10)
ex3=d>0
dd=dd-d*10
rs3=d>5
d=d-5*rs3
v3m=(d==3)
v3j=(d==4)
dd3=(d==2)+(d==4)
ex4=dd>0
rs4=dd>5
dd=dd-rs4*5
v4m=(dd==3)
v4j=(dd==4)
dd4=(dd==2)+(dd==4)
;
mm=trunc(da/100000)
da=da-mm*100000
d=trunc(da/10000)
ex0=d>5
ab=(d==2)+(d==7)
da=da-d*10000
d=trunc(da/1000)
w1=d>5
ab1=(d==2)+(d==7)
da=da-d*1000
d=trunc(da/100)
w2=d>5
ab2=(d==2)+(d==7)
da=da-d*100
d=trunc(da/10)
w3=d>5
ab3=(d==2)+(d==7)
da=da-d*10
w4=da>5
ab4=(da==2)+(da==7)
tt=ex0+ex1+ex2+ex3+ex4
;
d=imag(p2)
t=d<0
if (t)
d=-d
endif
dd=trunc(d)
d=round((d-dd)*10000000000)
pp=trunc(dd/100)/10
dd=dd-1000*pp
da=trunc(dd/10)
so1=((da==1)+(da==4)==0)
so2=((da==2)+(da==4)==0)
so3=((da==3)+(da==4)==0)
dd=dd-10*da
ir1=(dd==1)+(dd==4)
ir2=(dd==2)+(dd==4)
ir3=(dd==3)+(dd==4)
;
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
p8=trunc(d/100)/100
d=d-p8*10000
p9=d/100
;
d=real(p3)
mb=trunc(d)
ba=(d-mb)*100000
;
d=imag(p3)
sfac=trunc(d)
b1=(d-sfac)*100000
b0=b1/2
;
d=real(p4)
ofac=trunc(d)
b2=(d-ofac)*100000
;
d=imag(p4)
mi1=trunc(d)
fac1=(d-mi1)*100000
;
d=real(p5)
mi2=trunc(d)
fac2=(d-mi2)*100000
;
d=imag(p5)
mi3=trunc(d)
fac3=(d-mi3)*100000
;
bg=((ab+vb)==0)
bg1=((ab1+v1j)==0)
bg2=((ab2+v2j)==0)
bg3=((ab3+v3j)==0)
bg4=((ab4+v4j)==0)
;
if (d4)
z=0
if (vb)
c=0.4*log(sqr(pixel^mm))
else
c=pixel
z=pixel*(ab==0)
endif
else
if (bg)
c=p9
else
c=p1
endif
z=pixel
endif
t=0
u=d3
bo=z
p=pp
z0=p7
:
If (tt)
t=t+1
if ((ex0) && bo>b0)
u=2*(fn1(t/sfac))
if (d4)
z=z*u
if (vb)
c=0.4*log(sqr(pixel^mm))
ba=mb
else
c=pixel
endif
else
z=pixel
if (bg)
c=p9*u
else
c=p1*u
p=pp*u
endif
endif
ex0=0
tt=tt-1
elseif ((ex1) && bo>b1 && bo<b2)
if (w1)
u=2*(fn2(t/ofac))
else
u=1,0
endif
rs=rs1
ab=ab1
if (dd1)
if (rs)
z=pixel
endif
vb=v1j
d3=1
if (bg1)
c=p9*u
else
c=p1*u
p=pp*u
endif
else
d3=0
z=z*u
c=z
if (rs)
z=pixel*(ab==0)
endif
vb=v1m
if (vb)
if (so1)
mm=mm+mm
endif
c=0.4*log(sqr(pixel^mm))
ba=mb
endif
endif
if (ir1)
t=0
endif
ex1=0
tt=tt-1
elseif ((ex2) && t>mi1)
if (w2)
u=2*(fn2(t/fac1))
else
u=1,0
endif
rs=rs2
ab=ab2
if (dd2)
if (rs)
z=pixel
endif
vb=v2j
if (bg2)
c=p9*u
else
c=p1*u
p=pp*u
endif
d3=1
else
d3=0
z=z*u
c=z
if (rs)
z=pixel*(ab==0)
endif
vb=v2m
if (vb)
if (so2)
mm=mm+mm
endif
c=0.4*log(sqr(pixel^mm))
ba=mb
endif
endif
if (ir2)
t=0
endif
ex2=0
tt=tt-1
elseif ((ex3) && t>mi2)
if (w3)
u=2*(fn3(t/fac2))
else
u=1,0
endif
ab=ab3
rs=rs3
if (dd3)
if (rs)
z=pixel
endif
vb=v3j
if (bg3)
c=p9*u
else
c=p1*u
p=pp*u
endif
d3=1
else
d3=0
z=z*u
c=z
if (rs)
z=pixel*(ab==0)
endif
vb=v3m
if (vb)
if (so3)
mm=mm+mm
endif
c=0.4*log(sqr(pixel^mm))
ba=mb
endif
endif
if (ir3)
t=0
endif
ex3=0
tt=tt-1
elseif ((ex4) && t>mi3)
if (w4)
u=2*(fn4(t/fac3))
else
u=1,0
endif
ab=ab4
rs=rs4
if (dd4)
if (rs)
z=pixel
endif
vb=v4j
if (bg4)
c=p9*u
else
c=p1*u
p=pp*u
endif
d3=1
else
d3=0
z=z*u
c=z
if (rs)
z=pixel*(ab==0)
endif
vb=v4m
if (vb)
if (so2)
mm=mm+mm
endif
c=0.4*log(sqr(pixel^mm))
ba=mb
endif
endif
ex4=0
tt=tt-1
endif
endif
if (vb)
if (d3) ;quasinewton Pusk s Istv n
z1=z^p-1
z2=p*z*z
z=z-z1/z2
else
z2=fn1(z)+c ;many_mods Linda Allison
q=cos(z2)
z=c*(1-q)/(1+q)
endif
elseif (ab)
z2=z*z ;mandel Pusk s Istv n
z=z2*z2+p6*z2+c-p0
elseif (d3)
z1=fn1(z)-c ;bees Ray Girvan
z2=z1^p8-1
z3=p8*(z1^(p8-1))
z=z-(z2/z3)
else
z3=z ;secant unknown
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
}