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The past few months, real life has been very busy and left almost no time for fractal work. But in small increments, several big projects have finally been completed! One new video, Qbix, is finished, and the migration to 64-bit code is done as well.
Finally! In development since November, 2009, Qbix is done at last! This is the first deep-zoom animation into the cubic Mandelbrot set published on HPDZ, and as far as I can tell, it's the first cubic deep-zoom ever published anywhere. This video zooms in to a final size of 5.9E-33.
Here are a few sample images. Go ahead, look at them. Let your email client download the images. Come on. They're not going to bite you. Click on any one of them to go to the Qbix web page.
Qbix was originally conceived in November 2009. A series of test runs in early 2010 showed that rendering it frame-by-frame was not practical because calculating the third power of a complex number requires much more computational work than calculating the second power. rendered with frame interpolation to generate the 5000 video frames at 960x540 resolution from 181 larger master images using digital zooming techniques. Qbix was the first project created with the new 64-bit software (read on below), which significantly speeds up the calculation time.
Porting the core arithmetic code to 64-bit instructions is something I've considered for years, although I never really investigated whether doing so would result in speed increases over the previous 32-bit SSE2 code. Around the same time Qbix started to come to life, I began sketching out how 64-bit multiplication code would perform compared to the previous code, and I slowly put together some test assembly language code. Once it was clear that there was a significant speed gain to be realized, I went ahead and got the fractal rendering system set up to run Win7 and ported the whole fractal software system to the 64-bit platform. The entire story, with all the setbacks and the final speed improvement results, is detailed on a page in the Technical section of the website.
Life is going to continue to be extremely busy here at least until October, so there may not be much news until then. This may be a good time to just set the fractal system to rendering a very long, calculation-intenseive deep zoom. While in a trip to Seattle several months ago, I left my laptop drawing successively deeper zooms into a nice area of the Mandelbrot set. This should make a good deep zoom, and it looks like it will take a long time to calculate, so this is probably what will be coming next.
I've also been working on a formula I call "HyperNova", which is a slight modification of the well-known Nova fractal. I have made a few test videos of it, and it looks really good. We'll see if time permits any further work on this in 2010.
Interest remains high in extending the current fixed-point arithmetic code to floating-point. This will enable the software to take reciprocals of very small numbers, which will allow me to make deep-zooms into convergent-type fractals. This is a large project and it's unlikely there will be news on this until well into 2011.