Standard Shipping for delivery by Dec 24 has ended. Most products available with Express Shipping.

A bare bones spiral.

Mandelbrot algorithm, bad complex power, Gaussian Integer (ceiling) maximum angle.

Created using mars and expanded using phobos (see my public profile).

30th June 2011 – 4:3 ratio original replaced with a 3:2 ratio version

I’m a software engineer and I’ve been interested in the artists possibilities of fractals since about 1987. It wasn’t until 2010 that I started producing very high resolution pictures using my own software.

View Full Profile


  • Lemarly
    Lemarlyalmost 4 years ago

    Elegant fractal!

  • Bunny Clarke
    Bunny Clarkealmost 4 years ago

    This is gorgeous! I had no idea this is what the skeleton formula did. Gotta go try this one. Splendid work. :o)

  • Thank you, I’m glad you like it. I have no idea what the skeleton formula is.

    The formula I used for this has a bad implementation of complex power and as far as I know is unique to my programs. I know of at least three ways of writing a bad complex power function, I’ve implemented two of them and I may eventually get around to implementing the third. I discovered it by implementing it an OpenCL kernel so that the grapics card could do the calculations. An OpenCL kernel is based on C and doesn’t support complex types so I had to work out how to calculate the complex power of a complex number from first principles which involves conversion from cartesian coordinates to polar coordinates applying the power and converting back from polar coordinates to cartesian coordinates, I forgot to ensure when converting to polar that the angle was adjusted so that is in the correct quadrant. It was a happy mistake. In attempting to fix the problem I found a second bad complex power function which produced even more interesting images until I finally fixed it and found that the correct function produces very boring pictures indeed.

    Additionally as far as I know the colouring method using the maximum angle of a Gaussian Integer is also unique to my programs along with average angle and minimum angle.

    – Mark Eggleston

  • Junior Mclean
    Junior Mcleanalmost 4 years ago

    Thumbs up!!! Very cool!! :0)

desktop tablet-landscape content-width tablet-portrait workstream-4-across phone-landscape phone-portrait

10%off for joining

the Redbubble mailing list

Receive exclusive deals and awesome artist news and content right to your inbox. Free for your convenience.