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Magnet Deep 1

The first accurate HPDZ animation of a Magnet Fractal

Introduction

This video is a high-definition 1280x720 deep-zoom of the Magnet Fractal. It's one of only a very few animations of this type of fractal ever created. This video magnifies the fractal from an initial image size of 8.0 to a final images size of 2.64 x 10^-74, which is a magnification of 3.0x10⁷⁴. For some perspective on that number, see this discussion. Calculating the data for this fractal takes much longer than for the Mandelbrot set because the formula that generates it is much more complicated. This video took about 20 days to render.

The Magnet Fractal has an infinity of tiny Mandelbrot sets embedded in it, just like many other fractals that have similar underlying mathematical formulas. Many other visual elements in this fractal are also similar to what the Mandelbrot set has. But the Magnet Fractal has its own distinct features, especially the long arms of curled up detail, and the foamy look with large open spaces between.

In addition to the video captures below, some of the large primary images used to generate the animation are available for download. Click here or scroll down.

Video

In order to conserve limited server hosting space, the larger versions of this video are only available as MP4 files.

Background

A brief description of the origin of the magnet fractals, along with their generating formulas, is on the short still images page for them on this site. This animation is based on the type I Magnet Fractal.

The disappointing Magnet Zoom video published in the Fall 2010 issue forced a long-overdue radical update to the internal arithmetic code. Now true floating-point in high-precision is supported, and new Magnet Fractal deep zoom is the debut of this new code. A short non-deep zoom into the Magnet Fractal was published in Montage1.

Details

The 7200 frames of this video were generated by interpolation from 306 primary images (directly calculated from the fractal data) that range in size from 2932x1653 pixels to 2996x1689 pixels, with the exception of the final primary image, which is 1805x1019 pixels. The primary images are blended together with 25% overlap on the leading and trailing time segments. The weighted-averaging type of interpolation was used.

The music for this project is one of the SmartSound library pieces. It is an abstract amelodic piece of minimalist electronica that reminds me of some of the music of Stefan Betke aka Pole (external link), although without the distinctive "glitch" sounds in his music.

This animation uses one of the most complex colorizing palettes of any project on this site, with 14 individual color gradients. A global rank-order method was used to apply the palette across all the frames of the video.

Primary Data Images

In addition to the usual video captures that are published for every animation, this time I have included a sampling of the large primary images that are used for the interpolation. These are enormous uncompressed BMP files with different resolutions, but most are around 2950x1650 pixels. I included the first 5 primary images, then every fifth one after than, and then the final one, for a total of 66 images. Each fifth image is magnified about 17X from the previous one. The individual primary images are spaced apart about a factor of 1.75X.

Download a 443MB ZIP file with the images

In most browsers, right-click the above link and select Save

The coloring of these images is different from the video coloring. The same sequence of color gradients is used, but in the video, the fractal data is mapped into the color palette using a global set of data accumulated from all video frames. At present, the software cannot use the global data from a video to colorize an individual image file. There's nothing intrinsically impossible about this, but that ability needs to be written into the software, and that is definitely on the list of things to do on a free weekend. However, even if the exact color map that is used for the video were applied to these primary images, they would not be colored exactly like the corresponding video frames because the video frame images are a composite of overlapping primary images, and they are downsampled as well.