interactions {
; created by Bert van den Bosch
; note: put the bailout of the fractal at the most large value
; something like 10e80 will do
; please email me at zeusooooo@hotmail.com for questions or comments

init:


float t = 0.0
float tmpf = 0.0
float tmax=0
float s1 = 0.0
float s2 = 0.0
float s3 = 0.0

int iter = 0
int i = 0


complex tmp[8]
complex zhist[8]

while(i<@numhist)
    zhist[i] = #z
    i=i+1
endwhile

complex zz

loop:

zz = #z 


tmp[0] = (zz - zhist[0])

i = 1

while(i<@numhist)
    tmp[i] = (zhist[i] - zhist[i-1])
    i=i+1
endwhile



i = 0
s1 = 1.0
s2 = 1.0
s3 = 0.0


while(i<@numhist)

    s1 = s1*real(tmp[i])
    s2 = s2*imag(tmp[i])

    s3 = s3 + |tmp[i]|
    
    i = i+1
endwhile

tmpf = (@mix*s1+(1-@mix)*s2)/s3

if tmpf >tmax 
    tmax = tmpf
endif



t = t + tmpf

iter = iter + 1



i = @numhist

while(i>0)
    zhist[i] = zhist[i-1]
    i=i-1
endwhile


zhist[0] = zz


 final:
 
     if(@colorby == "average")
         #index =  t/(iter + 1 - log (log  (|#z|)) / log(2))
        ;#index =  (iter + 1 - log (log  (|#z|)) / log(2))
    
     elseif(@colorby == "maximum")
        #index = tmax
     endif
 
 default:
  title="interactions"
  
  param colorby
    caption="coloring"
    enum = "average" "maximum"

    default=0
    hint="color by"
  endparam
  


  param mix
    caption="mix"
    default=0.8
    hint="the weight on real or imaginary part of the generalized inner product"
  endparam


  param numhist
      enum = "1" "2" "3" "4" "5" "6" "7" "8"
    caption="history"
    default=3
    hint="dimension of the generalized inner product"
  endparam


}