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May has been a busy month. Two major new videos, and a large collection of new still images have been published. The Burning Ship fractal is definitely the fractal of the month, and likely of several months to come. But first, the Magnet Deep Zoom.
Magnet Fractal Deep Zoom
After the debacle of the previous Magnet Fractal zoom, major technical improvements were made in the core arithmetic routines of the software, and a new deep-zoom animation into the Magnet Fractal had to be made.
Click here to visit the MagnetDeep1 page.
This is a Hi-Def 1280x720 video that zooms to a final size of 2.6x10-74. It took about 20 days to calculate the 306 huge primary images that were interpolated to give the final video data. The coloring of this project is one of the most complex published so far here, with 14 individual color gradients making up the color palette.
And, for the first time, some of the actual primary images are being published with the video files. These are enormous, extreme high-definition uncompressed raw BMP images, most of which are approximately 2950x1675 pixels. Visit the MagnetDeep1 page (above link) for a link to a ZIP file to download.
Some sample images from the video are below. Click on one for the high-resolution original.
Burning Ship Images
The Burning Ship fractal goes way back to the early days of fractal art. Originally developed by Michael Michelitsch and Otto E. Rössler way back in 1992, this fractal is a close cousin of the Mandelbrot set, although it looks radically different. What the Mandelbrot set does with spirals, this fractal does with straight lines and angles. It is truly a remarkable treat for the eyes, and a completely different visual esthetic.
Click here to visit the Burning Ship page.
The function at the core of this fractal is just a slight variation on the Mandelbrot set's function. The details are a bit mathematical, and are described below. The subtle change results a very different visual effect, with hard lines and sharp angles as opposed to the Mandelbrot set's curlicues and spirals.
The fractal is named after the appearance of the main images in it, especially the mini-sets within the equivalent of the Western Antenna. This is best seen in the third image from the left in the top row below.
Many more images of this amazing fractal are on the still images page dedicated to it. Much more work on this will be forthcoming, including what is probably the first high-def high-precision deep zoom into this fracal ever created -- the Burning Ship Deep Zoom below.
Burning Ship Deep Zoom "Wallis"
In addition to the spectacular galleries of still images of the amazing Burning Ship fractal, HPDZ has also published the first-ever high-definition, 1280x720 deep-zoom animation into this fractal, to a final size of 2.34e-100. Below is a small sampling of a few frame captures of this incredible nearly 7-minute long animation.
A sampling of the primary images for this interpolated project is available for download, as with the Magnet Deep project. These are colossal 4400x2500 (approximately) pixel images that are the foundation of the 12,000 individual interpolated video frames of this project.
Click here to visit the Burning Ship Animation page
This project is named in honor of John Wallis, a 17th century mathematician who played a key role in providing intuitive, geometrical interpretations of negative numbers and complex numbers, among many other things.
This little test video has been languishing on a "demo" page. I went ahead and gave it a home.
Centanimus High-Quality Encodings
I found two hiqh-quality re-encodings of Centanimus that were made back in June 2010. They were just sitting there with no link to them, so I updated the Centanimus download table.
The Burning Ship fractal is based on iterating a formula very similar to the Mandelbrot set, but a little different. The Mandelbrot set it generated by iterating
z = z2 + c
which expands to
z = [Re(z) + i Im(z)]2 + c
The Burning Ship fractal is obtained by iterating
z = [|Re(z)| + i |Im(z)|]2 + c
The difference is the absolute values of the real and imaginary components are used in the Burning Ship fractal.