Burning Ship Fractal

Burning Ship Fractal – as seen on Paul Bourke’s web site :
xn+1 = xn2 – yn2 – xc, yn+1 = 2 |xn yn| – yc
This is really weird. I have no idea why it looks the way it does. It’s amazing what kind of pictures you can get with the right equations.
(* runtime: 5 minutes *)
BurningShip[zc_] := Length[NestWhileList[{#[[1]]^2 - #[[2]]^2, 2Abs[#[[1]]#[[2]]]} - zc &, {0, 0}, #[[1]]^2 + #[[2]]^2 < 200 &, 1, 250]];
DensityPlot[-BurningShip[{xc, yc}], {xc, 1.71, 1.8}, {yc, -0.01, 0.08}, PlotPoints -> 275, Mesh -> False, Frame -> False];


1 Response to “Burning Ship Fractal”

  1. 1 russel
    February 6, 2010 at 6:09 pm

    How does the (xc,yc) value affect this shape? I thought the initial starting point was (x0,y0) and we then moved the point and added this (xc,yc) vector. But then it looks like your code is varying the values of this vector so I’m really confused.
    Any comments would be greatly appreciated.
    Thanks in advance.

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