Site hosted by Angelfire.com: Build your free website today!

The Biomorph Fractal

f(z) = z⁷ + z⁵, c = 0.8

(to download a 1024x768 version of the image in TIFF format clic here)

You can create your own Biomorphs with the following utility:

Win32:	bioc.zip
Linux:	bioc.tgz
Source code:	browse or download

Example: bioc -R768,1024 -W3 -F2 -N5,0 -M7,0 -C0.8,0 bio.tif

z_n+1 = f(z_n) + c

Biomorph Species:: f₀(z) = sin(z) + e^z_re [cos(z_re) + i·sin(z_im)]; f₁(z) = z^N; f₂(z) = z^N + z^M; f₃(z) = z^z; f₄(z) = z^z + z^N; f₅(z) = sin(z); f₆(z) = sin(z) + z^N; f₇(z) = sin(z) + e^z; f₈(z) = sin(z) + B^z; f₉(z) = sin(z) + z^z; f₁₀(z) = tan(z) + z^N; f₁₁(z) = log(z) + z^N

The Perfect Flaw

The Biomorph comes from a bug in a program to calculate fractals. There was a flaw in the expression that checks if a point belongs to the convergence set. In that expression an AND operation was mistaken by an OR, broadening the set of points that matched the test...
The strange function f₀(z) also comes from a bug in the implementation of the Biomorph algorithm. This time the flaw was in the expression to calculate the complex term e^z, that was erroneously expanded as:
e^z_re [cos(z_re) + i·sin(z_im)]
instead of the correct way:
e^z_re [cos(z_im) + i·sin(z_im)]
It happened that this flawed expression resulted in an interesting fractal...

Home