Multifractal_7

26 Jul 2003

      Hi,

the new multifractal edition now has 8 formulas to choose, a
phoenix type is now available and a spider type. The maximum
now has been reached concerning the structure of the formula
and the possible amount of inputs.
Another fundamental improvement is that the "warp-effect" now
is used in two different ways: If reset is checked "z" is set
to the basic value and the effect, if enabled, is applied to
the input. If reset is not checked the effect, if enabled,
is applied to "z" which generates a different image, of course.
This means a whole lot of new possibilities and is especially
useful in case of sensitive inputs such as Julia, Spider,
Phoenix. So there are four different ways to control each
in/out part of the image, with or without reset and with or without
thw warp-effect, which by itself can be modified in many ways.

Fractal greetings,
Al

--------------------------------start-frm----------------------
FRM:Multifractal_7    { ;  Albrecht Niekamp  240703
;p1 (spider)julia-seed
;real(p2) 5digits: frm-use: shape, outside, inside1, inside2, inside3
; 0_off 1_secant/mand 2_bees/jul 3_m_mods/phoen 4_newt/spider +5_reset
;  input2 : 2digits_many-mods  2digits_phoenix  2digits_spider
;           5digits_secondary frm use : 0_no 1_yes +5_warp
;imag(p2)(-) 2-4digits : quasinewton input (max 2000)
;               1digit : no many_mods multipl. 1_out 2_in1 3_in2 4_all
;               1digit : iter-reset 1_out 2_in1 3_in2 4_all
;  input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees
;real(p3) many_mods bailout, bailout
;imag(p3) shape   : factor (fn1), outside : border-in (5digits+fract)
;real(p4) outside : factor (fn2), border-out (5digits+fract)
;imag(p4) inside1 : maxiter1, 5digits_factor1 (fn2)
;real(p5) inside2 : maxiter2, 5digits_factor2 (fn3)
;imag(p5) inside3 : maxiter3, 5digits_factor3 (fn4)
;fn(1) is shared by many_mods, bees
da=real(p2)
dd=trunc(da)
da=round((da-dd)*100000000000)+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/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
ab=(d==2)+(d==7)
da=da-d*10000
d=trunc(da/1000)
w1=d>4
ab1=(d==2)+(d==7)
da=da-d*1000
d=trunc(da/100)
w2=d>4
ab2=(d==2)+(d==7)
da=da-d*100
d=trunc(da/10)
w3=d>4
ab3=(d==2)+(d==7)
d=round(da-d*10)
w4=d>4
ab4=(d==2)+(d==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
;
mo=vb>ab
mo1=v1m>ab1
mo2=v2m>ab2
mo3=v3m>ab3
mo4=v4m>ab4
;
sc=((ab+vb)==0)
sc1=((ab1+v1m)==0)
sc2=((ab2+v2m)==0)
sc3=((ab3+v3m)==0)
sc4=((ab4+v4m)==0)
;
px=((ab+vb)==2)
px1=((ab1+v1m)==2)
px2=((ab2+v2m)==2)
px3=((ab3+v3m)==2)
px4=((ab4+v4m)==2)
;
if (d4)
 z=0
 if (vb)
  if (mo)
   c=0.4*log(sqr(pixel^mm))
  else
   c=pixel
   z=pixel
  endif
 else
  c=pixel
  z=pixel*sc
 endif
else
 c=p1
 z=pixel
endif
t=0
u=d3
bo=z
p=pp
z0=p7
zold=(0.0,0.0)
cb=p9
:
If (tt)
 t=t+1
 if ((ex0) && bo>b0)
   u=2*(fn1(t/sfac))
   if (d4)
    z=z*u
    if (mo)
     c=0.4*log(sqr(pixel^mm))
     ba=mb
    else
     c=pixel
    endif
   else
    z=pixel
    cb=p9*u
    c=p1*u
    p=pp*u
   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
     cb=p9*u
     c=p1*u
     p=pp*u
    else
     c=p1
     z=z*u
     cb=p9
    endif
    vb=v1j
    d3=1
   else
    d3=0
    if (rs)
     c=z*u
     z=pixel*(sc1+px1)
     z0=p7*u
     ph=ph*u
    else
     c=z
     z=z*u
    endif
    vb=v1m
    if (mo1)
     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
     cb=p9*u
     c=p1*u
     p=pp*u
    else
     cb=p9
     c=p1
     z=z*u
    endif
    vb=v2j
    d3=1
   else
    d3=0
    if (rs)
     c=z*u
     z=pixel*(sc2+px2)
     z0=p7*u
     ph=ph*u
    else
     c=z
     z=z*u
    endif
    vb=v2m
    if (mo2)
     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
     cb=p9*u
     c=p1*u
     p=pp*u
    else
     cb=p9
     c=p1
     z=z*u
    endif
    vb=v3j
    d3=1
   else
    d3=0
    if (rs)
     c=z*u
     z=pixel*(sc3+px3)
     z0=p7*u
     ph=ph*u
    else
     c=z
     z=z*u
    endif
    vb=v3m
    if (mo3)
     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
     cb=p9*u
     c=p1*u
     p=pp*u
    else
     cb=p9
     c=p1
     z=z*u
    endif
    vb=v4j
    d3=1
   else
    d3=0
    if (rs)
     c=z*u
     z=pixel*(sc4+px4)
     z0=p7*u
     ph=ph*u
    else
     c=z
     z=z*u
    endif
    vb=v4m
    if (mo4)
     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)
  if (ab)
   z=z*z+c                                ;Spiderjul     John Horner
   c=c*sp+z
  else
   z1=z^p-1                               ;Qusinewton    Pusk s Istv n
   z2=p*z*z
   z=z-z1/z2
  endif
 elseif (ab)
   zt=z*z+ph-0.5*zold                     ;Phoenix       Mike Wareman
   zold=z
   z=zt
 else
  z2=fn1(z)+c                             ;Many_mods     Linda Allison
  q=cos(z2)
  z=c*(1-q)/(1+q)
 endif
elseif (d3)
 if (ab)
  z2=z*z                                  ;Julia         Pusk s Istv n
  z=z2*z2+p6*z2+c-p0
 else
  z1=fn1(z)-cb                            ;Bees          Ray Girvan
  z2=z1^p8-1
  z3=p8*(z1^(p8-1))
  z=z-(z2/z3)
 endif
elseif (ab)
 z2=z*z                                   ;Mandel        Pusk s Istv n
 z=z2*z2+p6*z2+c-p0
else
 z3=z                                     ;Secant        Mike Wareman
 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
}

-------------------------------------------start-par---------------------
downmix            { ; inside spider-newton-phoenix
                     ; Albrecht Niekamp  July, 03
                     ;
                     ;
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=cos/exp/exp/exp passes=t
  center-mag=0.453671/1.33227e-015/1.323725/1/-90/3.88578058618804789e-016
  params=-0.02237006744590594/-0.07473982970671712/10498.32595010101/5000.\
  0608020602/2048.04084/384.0000045/384.00024/256.0076800000001/512.007680\
  0000001/768.0076800000001 float=y maxiter=2048 inside=maxiter
  outside=tdis logmap=4 periodicity=0 rseed=-2436
  colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\
  q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\
  0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455
  }

spinewphoesec      { ; Albrecht Niekamp  July, 03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=cos/exp/exp/sin passes=t
  center-mag=-8.88178e-016/-8.88178e-016/1.041667/1/-90/3.8857805861880478\
  9e-016
  params=-0.02237006744590594/-0.07473982970671712/40986.3259501001/5000.0\
  608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/1\
  024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4
  periodicity=0 rseed=-2436
  colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\
  q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\
  0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455
  }

Secantflyer        { ; Albrecht Niekamp  July, 03
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=cos/exp/exp/sin passes=t
  center-mag=0.312805/0/0.6666667
  params=-0.02237006744590594/-0.07473982970671712/31997.32595010605/5000.\
  0608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/\
  1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4
  periodicity=0 rseed=-2436
  colors=2000gt<22>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3\
...
000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkl\
  l<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0dq0es<3>0kz0jx0hv
  }
Double_image       { ; Time 0.19.43.53
                     ; Albrecht Niekamp  July, 03
                     ;
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t
  center-mag=0.426332/6.66134e-016/1.344086/1/-90/-1.23373533611470521e-01\
  4
  params=-0.02237006744590594/-0.07473982970671712/10482.64595310601/5040.\
  0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\
  12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis
  periodicity=0 rseed=-2436
  colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\
  unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\
...
eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\
  0dq
  }
Layers             { ; of the onion
                     ; Albrecht Niekamp  July, 03
                     ; Time 1.33.03.85
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t
  center-mag=0.972387/-0.248155/26.88172/1/-90/-1.23373533611470521e-014
  params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\
  0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\
  12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis
  logmap=yes periodicity=0 rseed=-2436
  colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\
  unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\
...
eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\
  0dq
  }
Hanging_gardens    { ; of Semiramis
                     ; Albrecht Niekamp  July, 03
                     ; Time 0.48.12.55
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t
  center-mag=+0.36133792768156270/-0.64229253619003070/116197.8/1/-90/3.88\
  578058618804789e-016
  params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\
  0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\
  12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis
  periodicity=0 rseed=-2436
  colors=2000JQ<12>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\
...
e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\
C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<10\
0IO
  }
mm_meets_spider    { ; Time 0.36.26.15
                     ; Albrecht Niekamp  July, 03
                     ;
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t
  center-mag=+0.36139649738980650/-0.64231765276418100/11619.78/1/-90/-1.2\
  3373533611470521e-014
  params=-0.02237006744590594/-0.07473982970671712/10482.64595110656/5040.\
  0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\
  12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis
  logmap=3 periodicity=0 rseed=-2436
  colors=200555<20>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\
  o0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\
  unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222\
  444
  }

Ying&Yang          { ; Time 0.19.14.27
                     ; Albrecht Niekamp  July, 03
                     ;
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t
  center-mag=+0.38684901922323730/-0.63969404719008790/37.1833/1/-90/-1.23\
  373533611470521e-014
  params=-0.02237006744590594/-0.07473982970671712/10437.32595910656/5000.\
  0608020602/82048.02048000001/384.0000045/384.00024/128.00768/190.0076800\
  000001/384.0076800000001 float=y maxiter=3072 inside=maxiter
  outside=tdis logmap=3 periodicity=0 rseed=-2436
  colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\
  A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875\
  <3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn
  }

The_Brain          { ; Time 0.02.53.45
                     ; Albrecht Niekamp  July, 03
                     ; Shape Phoenix
                     ;  Version 2002 Patchlevel 5
  reset=2002 type=formula formulafile=mfr.frm
  formulaname=multifractal_7 function=sin/sin/exp/sin passes=t
  center-mag=0/0/0.6666667
  params=-0.02237006744590594/-0.07473982970671712/32946.32595710155/5000.\
  0608020602/2048.04094/384.0001645/384.00048/128.00768/384.0076800000001/\
  512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis
  logmap=4 periodicity=0 rseed=-2436
  colors=200033021000<4>984BA5DC6FE7HF8JH9<13>jeNlgOniPpjQrlRtnS<2>ysW<25>\
  BB6995774553442220000<24>n00p00r00<3>y00<25>B00900700<3>000221<4>9A9BCBD\
  EDFGFGHG<15>hihjkjklk<3>rsr<21>HIHFGFEFE<3>676454343121000<25>0bn0dp0er<\
  3>0ky<28>055
  }

----------------------------------------------------------------------------
----end-----------------------

Albrecht.Niekamp＠t-online.de

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