hpdz.net

High-Precision Deep Zoom

Still Images

Early deep zoom images
	"Metaphase". The coordinates for this image are from a FractInt PAR file by Paul Derbyshire, dated 14 Mar 1996, and the title is his. It was incredibly clever of him to locate something like this, especially considering the hardware that was available in the early/mid-90's. This is one of my first deep zoom images. I have since created some animations that zoom into this location. The top thumbnail links to the earliest image (Jan 14, 2002) of this location that I can find on my system, which is rather small. The bottom thumbnail links to a high-resolution 2000x1600 image from April 2004. The size of the images is 5.0e-30. The bottom image does not use the exact coordinates form the original PAR file, but rather is at a slightly different location. Still, it looks essentially identical to the image at the original coordinates.
	Continuing to zoom in to the Metaphase structure above. The exact magnification is unknown.
	My first image deep zooming into a mini-brot on the zero axis. This area is a rich source of relatively easy deep zooms since the iteration count tends to remain fairly low as you zoom in compared to other areas in the set. I think the "40a" in the title refers to E40 being the magnification, although I don't have any documentation to confirm this. The "prec6" in the title means that 160 bits were available, which means it must be less than E48 for sure.
	Zoom41 must refer to the size of the image being E41. This is dated Jan 15, 2002 and is also a mini-brot on the zero axis. It reminds me of the "horizontal hold" image that was generated long ago by the real pioneers of deep zoom imaging of the Mandelbrot set, although this image is nowhere near that level of zooming.
	My first deep zoom into the main cusp, an area which turned out to be my favorite for many years, so much so that it is going to get its own whole page soon. There is incredible richness of structure here and the spirals and pods always manage to arrange themselves in the most amazing patterns. Unfortunately, the iteration counts go up extremely fast in this area and it is very difficult to generate animations here.
	Jan 20, 2002. This image is a deep zoom to 1.9e-15 in the cusp. It's only interesting to me because it's the first one where the BMP file name matches the historical log file name, so I can be sure I know where it is and what its zoom factor is. It's pretty but not spectacular. This is from the period where I was in love with the RGB-violet color palette.
	Finally breaking away from the RGB palette. Another image from the cusp, 6e-15 deep zoom.
	Jan 20, 2002. The deepest zoom up to this point in the past. The size is 4.6e-45.
	Jan 23, 2002.I have no idea anymore why this was called "test image", but you have to love the distance estimator's cool dwell bands. You can still see the bright banding from the linear color palette interpolation. The location and zoom of this image were not recorded.
	Feb 9, 2002. Three different colorings of a modest deep zoom to 2.37e-32. These images are some of my favorite. Consider each of the tiny little barely-visible spirals around the mini-brot in the center. Each of them has thousands of is its own little spirals and M-sets, going on deeper and deeper forever. It's sometimes easy to ignore the staggering magnitude of the depth of zooms of these images, but this one always makes me just pause and contemplate the profound, awesome magnitude of this object. It also makes me think how little of it has really been explored. What's in those arms? How different is one arm from another? How do the images in the green area differ from the images in the pink area? This could go on forever, and the same mini-brots keep appearing, with an almost psychotic relentlessness. And this all comes from that one simple little quadratic polynomial. It's so simple that it is probably universal--if there is life on other planets, or if life evolves in another Universe, it is almost certain they will discover exactly these same images.

Note on size and magnification: The sizes here (and on the Animations page) are the actual size of the smallest dimension of the image (usually vertically) in the complex number plane. Some programs describe image sizes by "magnification" which is usually related to the reciprocal of the image size. A size of, say, 1E-100 corresponds to a magnification of 1E+100. Some software uses the half-height of the image, so there may be an additional factor of two involved in conversion.