Re: [Fractint] An afternoon visiting an old friend.

21 Jan 2003

      Hi Morgan,

At 19:54 14/01/03 +1300, you wrote:
...
Guess I should have seen it coming...
me too.. super formulas! super pic's! lot's of stuff to play around..
wouwww!!
...
Morgan L. Owens
"Now, to the theatre."
here's something for 3D freaks..

run the pic, enter the evolver, leave all values on default except these: 

Param 1 real=no
Param 1 imag=no
Param 2 real=no
Param 2 imag=x+y (or x-y or x)

image grid size=5 

for parallel eyed viewing:

x parameter range=4
x parameter offset=-2

for crossed eyes viewing:

x parameter range=-4
x parameter offset=2

if the 3D effects are too strong, press F2 to halve the mutation levels..

*************

evolve3d           { ; Version 2002 Patchlevel 3
  reset=2002 type=formula formulafile=fractint.frm
  formulaname=threecircles2
  center-mag=-1/0/0.33/1/-90/0
  params=0.4/0/-2.5/0 float=y maxiter=200 inside=atan outside=atan
  periodicity=0
  colors=000000<57>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`\
  uR`v<2>SbyTczSby<61>000
  }

; and the formula again (I don't know the author of it; maybe from Morgan
L. Owens)

frm:threecircles2 {
centre1=1
centre2=exp(flip(2*pi/3))
centre3=sqr(centre2) 
rho=real(p1)
direction=pixel-p2
z = pixel
trapped=(|z-centre1|<sqr(rho) || |z-centre2|<sqr(rho) || |z-centre3|<sqr(rho))
: 
if(trapped)
   escaped=0 
else 
   escaped=1 
   hit=9999 
   coefA = |direction|
   coefB = real(z-centre1)*real(direction)+imag(z-centre1)*imag(direction)
   coefC = |z-centre1|-sqr(rho)
   discriminant=coefB*coefB-coefA*coefC
   if(discriminant>0) ; Two solutions
     t1=(-coefB-sqrt(discriminant))/coefA
     t2=(-coefB+sqrt(discriminant))/coefA
     if(t1>0) 
       escaped=0
       hit=t1
       target=1 
     endif
     if(t2>0 && t2<t1)
       escaped=0
       hit=t2
       target=1
     endif
   endif
   coefB = real(z-centre2)*real(direction)+imag(z-centre2)*imag(direction)
   coefC = |z-centre2|-sqr(rho)
   discriminant=coefB*coefB-coefA*coefC
   if(discriminant>0)
     t1=(-coefB-sqrt(discriminant))/coefA
     t2=(-coefB+sqrt(discriminant))/coefA
     if(t1>0 && t1<hit)
       escaped=0
       hit=t1
       target=2
     endif
     if(t2>0 && t2<t1 && t2<hit)
       escaped=0
       hit=t2
       target=2
     endif
   endif
   coefB = real(z-centre3)*real(direction)+imag(z-centre3)*imag(direction)
   coefC = |z-centre3|-sqr(rho)
   discriminant=coefB*coefB-coefA*coefC
   if(discriminant>0)
     t1=(-coefB-sqrt(discriminant))/coefA
     t2=(-coefB+sqrt(discriminant))/coefA
     if(t1>0 && t1<hit)
       escaped=0
       hit=t1
       target=3
     endif
     if(t2>0 && t2<t1 && t2<hit)
       escaped=0
       hit=t2
       target=3
     endif
   endif
   if(target==1)
    un=(z-centre1)/cabs(z-centre1)
   elseif(target==2)
    un=(z-centre2)/cabs(z-centre2)
   else
    un=(z-centre3)/cabs(z-centre3)
   endif
   r=direction-2*(real(direction)*real(un)+imag(direction)*imag(un))*un
   z=z+direction*hit
   direction=r
endif
escaped==0
}

***********

have fun,

Guy

Re: [Fractint] An afternoon visiting an old friend.

Guy Marson