comment {
  Davka's coloring algorithms
  
  - SpeedAccel provides parameters
    for gradient speed and acceleration
    in the style of Fractal Extreme.
}

SpeedAccel {
; 12Aug02 Davka
 
final:
  float normiters = real(#numiter) / 100.0  ; "normalized" iteration count
  float normmax = real(#maxiter) / 100.0    ; "normalized" max # of iterations
  
  ; Early attempts, rejected
  ; #index = normiters / @speed * (1 + normiters / normmax * (@accel - 1))
  ; #index = normiters / @speed + normiters / normmax * (@accel - 1)
  ; #index = (normiters / @speed) ^ (@accel - 1)

  ; The linear portion of the equation is (normiters / @speed).
  ; The linear portion is divided by (1 + normiters / normmax) ^ (@accel - 1).
  ; (1 + normiters / normmax) is always a value between 1 and 2.
  ; When @accel = 1, (1 + normiters / normmax) ^ (@accel - 1) = 1.
  ; As @accel increases, it increases the value of (1 + normiters / normmax) ^ (@accel - 1),
  ; which "slows" the application of the gradient.
  #index = (normiters / @speed) / (1 + normiters / normmax) ^ (@accel - 1)
      
default:
  title = "SpeedAccel"
  
  param speed
    caption = "Speed"
    default = 1.0
  endparam
  
  param accel
    caption = "Acceleration"
    default = 1.0
  endparam
}