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Secant Animation 1 is finally completed.

This is, as far as I am aware, the second-ever fractal animation published that uses the secant method to generate the fractal (the first was Secant Animation 2).

This video is a tour of the fractal with static parameters, rather than a parameter roll like SA1. It's about 4.8 minutes long. The basic underlying math formula is the secant method for finding roots applied to finding the roots of cos(x)=0.

Two major technical accomplishments went into creating this.

First, the control of the motion of the viewpoint and zoom has been greatly improved to allow me to make very smooth, seamless simultaneous pan/zoom movements. Eighteen key frames were chosen to define viewpoint location and magnifications, and the movement was interpolated between them.

Second, the colorization has been improved to give me manual control over how the count-to-color mapping changes with time as different portions of the fractal come in and out of view. I had previously tried several fairly sophisticated digital filtering methods to try to automatically generate the parameters for the color mapping, but really fine-tuning this manually works best. The trade-off here is extreme under-utilization of the available color palette versus rapid shifts in the color mapping creating annoying color-roll effects. You can see the worst area of color under-utilization around time index 4:10, where most of the image turns orange. The data here is just moves through such an extreme shift in dynamic range that this was the best I could do without introducing severely disturbing wild color palette rolls. I think I've found a way to do this, still under development.

I also decided to render it in 16:9 video format since there are lots of wide structures in this fractal.

Enjoy!

This is the web page with the high-quality video files (4 Mbps, 800x450, 30fps).


If there's interest, I can upload a 10 Mbps MP4 file which looks nearly as good as the uncompressed video, but it's 385 MB.

Also available on YouTube:
<a href="http://www.youtube.com/v/diaM1Lsc3vg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/diaM1Lsc3vg&rel=1&fs=1&hd=1</a>

Thanks, bib. This fractal is incredibly intricate and diverse, with no two areas looking quite the same.

Unfortunately, the still image from it doesn't seem to be doing too well in the 2D image competetion , but then, there are some really gorgeous entries to compete with.

Thanks very much.

Brilliant stuff. Love the colors. Hope to see some more of that kind. Keep up the great job HPDZ.

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