Fractal Fish

[mjk1093]

Thought these were neat!



Link for bigger image: http://i.imgur.com/KmNNx.png

Formula: z_n+1=z_n²+z_n-1²+z_n-2²+c

[kram1032]

cute! 

[Timeroot]

Formula: z_n+1=z_n²+z_n-1²+z_n-2²+c

Mandel or Julia? 

[mjk1093]

Mandel or Julia?  

Mandel, as indicated by the "c" instead of a specific number. At least I think that's the convention? I'm rather new at this but having a lot of fun! There's a lot of other interesting stuff in that region too. The coordinates are (-0.42421875, -0.35729166667) magnification 275. Here's the code I used in UltraFractal to get the z_n-1 and z_n-2 recursive elements:

{
init:
  z = 0
  a = 0
  b = 0
loop:
  z = z^@power + a^@power2 + b^@power3 + #pixel
  c=b
  b=a
  a=z
bailout:
  |z| < @bailout
default:
  float param bailout
    default = 1000
    min = 1
    exponential = true
  endparam
  param power
     default = (2,0)
  endparam
  param power2
     default = (2,0)
  endparam
  param power3
     default = (2,0)
  endparam
}

There's a lot of interesting stuff if you set power2=(3,0) and power3=(3,0) as well.