Adjusting the branch cut

The second image in this post was quite popular, so I decided to make a movie out of it.

There aren't really many parameters in the equations used to make this image, though - (the functions are just negative, exponential and logarithm). The colouring is arbitrary but modifying it wouldn't make a very interesting movie. The zoom factor is fairly arbitrary as well but zooming very much in or out would make the image take much longer to render (besides which, zooming movies have been done to death). About the only other arbitrary thing about the image is the choice of branch cut for the logarithm.

This describes a way of adjusting the branch cut in a continuous way, and this is the movie I made by adjusting theta from -4.5 to +4.5 radians:

High quality 640x480 11Mb DivX avi version.

This took about three days to render. I could have done it faster, but my laptop gets uncomfortably warm when both its cores are fully utilized. Also, a problem with Vista networking was causing the other machine I was using to keep getting disconnected from my laptop every few frames.

One Response to “Adjusting the branch cut”

  1. [...] video I made for Saturday’s post made me wonder what the picture would look like if you didn’t have a branch cut at all - if [...]

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