Hi,
this is a MOST unsusual
image. Got it using border-out
values for bailout instead of border-in.
The In-version is a pretty multistructural
one and then this. Can anybody tell me
what happened? Invisible mandels seem to
be outside with their heads turned
to the inside.
Jim, or Paul, if listening, what do you think?
Note the FRM version with an improved
input section.
Albrecht
-----------------------start-par------------------
71635x             { ; Mystery
                     ; time 28.57 1600/1200
                     ; Newt-secant-phoen-bees-mmods
  reset=2004 type=formula formulafile=mfr_10.frm
  formulaname=multifractal_10
  function=cos/exp/exp/sin passes=t
  center-mag=0.0104739/-0.881323/3.318983/0.8831
  params=-0.05825983458967864/0.3785210730307932/716\
  35.03564901002/14253.2207090221/151024.0204808192/\
  384.32768524288/384.00482000595/128.3007681001/256\
  .3007682001/512.3007683001 float=y
  maxiter=3072 inside=maxiter outside=tdis
  logmap=-4 periodicity=0 rseed=-2436
  colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\
  J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\
  tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\
  6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\
  4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\
  y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\
  W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\
  lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\
  8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\
  6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\
  _5fc0ce7_jFRoNIzb0zj0000zr0
  }
frm:multifractal_10    { ;  Albrecht Niekamp  Jan2005
;RP2 Left:5 Dig_Chan: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3
;     Frm:0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_phoen 7_newt 8_spid
;   Right:2 Dig_MMods_Number of sides  2 Dig_Phoenix  2 Dig_Spider
;         1 Dig_TransReset-Shape: 0_no 1_DblMand 2_Iter-res 3_both +5_warp
;         4 Dig_TransReset-Ch 2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp
;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5
;   Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees
;RP3 Left: 2 Digits_Newtonvariable  4 Digits_Colour1
;   Right: 5 Digits_Colour2  5 Digits_Colour3
;IP3 Left: Shape: Warp-factor (fn1 is used)
;   Right: 5 Digits_Colour4  6 Digits_Colour5
;RP4 Left: Outside: Warp-factor (fn2 is used)
;   Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in
;IP4 Left: Inside1_Maxiter
;   Right: Inside1_Transition: 1_maxit  2_bordout  3_bordin  +5_maxit+bord
;          5 Digits_warp factor (fn2 used)  4 Dig+1 fractaldig_border1
;RP5 Left: Inside2_Maxiter
;   Right: Inside2_Transition: 1_maxit  2_bordout  3_bordin  +5_maxit+bord
;          5 Digits_warp factor (fn3 used)  4 Dig+1 fractaldig_border2
;IP5 Left: Inside3_Maxiter
;   Right: Inside3_Transition: 1_maxit  2_bordout  3_bordin  +5_maxit+bord
;          5 Digits_Warp factor (fn4 used)  4 Dig+1 fractaldig_border3
;  Altnat: Left: 1_Lake effect enabled (Inside3 disabled)
;         Right: 2 Digit_Frequency  2 Digit_Waterlevel  2 Digit_Amplitude
;
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)     ;lake effect by S.Gallet
 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)                                ;Spider
   c=p1
  else
   z=z*le+pixel*(le==0)
   c=p1                                                ;newton
  endif
 elseif (ab)
   c=z                                                 ;Phoenix      
   z=z*le+pixel*(le==0)
  else
   c=0.4*log(sqr(z^mm))                                ;many mods
   z=0
 endif
elseif (d3)
 if (ab)
  c=p1                                                 ;Julia        
  z=z*le+pixel*(le==0)
 else                                                  ;bees
  c=p1
  z=z*le+pixel*(le==0)                               
 endif
elseif (ab)
 c=z                                                   ;Mandel
 z=0
else
 c=z                                                    ;Secant     
 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                           ;Spiderjul     John Horner
   c=c*sp+z
  else
   z1=z^p-1                          ;Quasinewton    Puskas Istvan
   z2=p*z*z
   z=z-z1/z2
  endif
 elseif (ab)
   z1=z*z+0.56+ph/100-0.5*zold       ;Phoenix       Mike Wareman
   zold=z
   z=z1
 else
  z2=fn1(z)+c                        ;Many_mods     Linda Allison
  z1=cos(z2)
  z=c*(1-z1)/(1+z1)
 endif
elseif (d3)
 if (ab)
  z2=z*z                             ;Julia         Puskas Istvan
  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)
 if (dm)
   z=z*z+c+c*c-dp                    ;Double Mandel
 else
  z2=z*z                             ;Mandel        Puskas Istvan
  z=z2*z2+p6*z2+c-p0
 endif      
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
}