I've always been fascinated with fractals since I read the cover article "Exploring the Mandelbrot Set" in the August 1985 issue of Scientific American. I knew nothing about fractals at the time so this article was kind of a revelation to me. I assimilated the underlying math and quickly wrote a program for the HP-150 Touchscreen computer in Turbo Pascal, which could render the Mandelbrot set in 9 ersatz shades as well as zoom into it. Then Windows 3 was introduced and I wrote a Windows program in C which did the same, but it was a real chore as I had to work at a very low level, calling the Windows API for everything (message processing, etc) in a pure text environment, no GUI for the C editor/compiler. Then VB was released and I wondered if using it would make a difference.
It did. The VB program ran 7x slower but developing it was 7x faster and much easier and convenient, real fun instead of real chore. That was it back then but 30 years later (2016) I found the VB program in an old HDD and tried it on my Windows XP. It ran, but it was extremely limited, rendering just the original Mandelbrot set in 16 colors with minimal zoom capabilities and that's it. I then decided it would be fun to try and relive the old times by writing a new, more capable fractal program just for my own use, and using the very same 30-year old, 16-bit programming language and 20-year old, 32-bit OS absolutely from scratch, beginning from a blank form and nothing else. The result is FractVal 1.0, which follows these guidelines:
A simple formula, a simple palette and a simple rendering algorithm.
And that's it. The images FractVal produces can be described and recreated with few parameters because they do not depend on artistic choices or techniques, they're renderings of mathematical objects mostly independent of who's generating them: the palette may be specified, it may be rendered with one simple algorithm or another but the resulting image will essentially depend on the fractal object itself. Last but not least, they're indefinitely explorable and you'll actually feel The Call of Discovery: "To eagerly find amazing locations no one has ever seen before". Literally (and if you don't record their parameters no one will ever explore them again. Literally.).
This is an approximate FractVal rendition (from memory) of the very first fractal image I saw in the cover of the August 1985 issue of Scientific American. The palette and framing will surely be a little different from the original cover but the impression it made on me is the same, a sheer feeling of awe and fervent desire to do my own exploring of it.
The SA's article itself, "Exploring the Mandelbrot Set", was a fantastically enthralling read (look for it, it's freely available on the net), which gave lots of useful explanations that helped me to soon after write my very own program to render this most fascinating set. It was very primitive but it was a beginning and FractVal is just the latest step so far.
This is not an image but an example of one of the types of videos that FractVal can generate. Many fractal programs can generate videos, but usually they are of what I call the "static" kind, i.e: (I) the video will zoom into/out of the fractal object or it will pan from one part to another, or a combination of both, or (II) they will also generate videos where the palette is cycled or altered in some way or another, making the fractal object change colors or lighting continuously or after some other fashion.
This is all very well and very nice, and of course FractVal can also generate those kinds of videos, but notice something important: the fractal object is static, it does not vary at all while the video runs. You see different parts of it at different zoom levels and/or with different palettes but the fractal object does not essentially change, it might be distorted or a false perspective might be added but it stays put, it doesn't evolve, it's absolutely static, frozen in time for the video's duration.
ValFract, on the other hand, can generate a Type III kind of video, where the fractal object itself isn't static but evolves as the video goes on, it doesn't remain the same, it changes or moves on its own, it's alive. While other fractal programs show you just pretty pictures of an instant in the life of a fractal, static pictures, FracVal allows you to explore The Secret Life of a Fractal and see what it does and what happens to it. And of course, you can mix this fractal activity with zooms, pans, palette changes and whatever for incredibly beautiful and truly amazing results.
In this particular Sample Video, titled "Cellular Genesis", you can watch a few scattered figments of DNA beginning to slowly evolve, to combine and form ever-complex cells, true evolution in a mathematical fractal universe. And remember, each frame is a static image which can be indefinitely zoomed, potentially having all the infinite detail of the fractal object it renders.
For filesize and server space reasons this sample video has frames about 16 times smaller than the original I made, and it runs at 10 fps instead of 25 fps, plus other size-related limitations, but it will certainly give you a very good idea of what's possible. Video details: 12.8 Mbytes, 40 seconds long, 320x240 frames at 10 fps, DivX format in an .avi container).
This is an example of one of the types of videos that FractVal can generate, Type I, the variant where the video features a fractal object being zoomed-in or out at some speed. In this particular video the original Mandelbrot fractal is zoomed-in at a very fast speed.
For filesize and server space reasons this sample video has frames about 4 times smaller than the original I made and it runs at 20 fps instead of 25 fps, plus other size-related limitations which affect quality, but it will give you a good idea of what's possible. Video details: 5.08 Mbytes, 12 seconds long, 640x480 frames at 20 fps, DivX format in an .avi container).
This is an example of one of the types of videos that FractVal can generate, Type II, the variant where the video features a fractal object whose palette is being rotated or altered in some way at a certain speed to generate a number of effects, such as ever-changing lighting and such. In this particular example a cute denizen of the fractal universe changes looks fast.
For filesize and server space reasons this sample video has frames about 4 times smaller than the original I made and it runs at 14 fps instead of 25 fps, plus other size-related limitations which affect quality, but nevertheless it will give you a decent idea of what's possible. Video details: 3.3 Mbytes, 16 seconds long, 640x480 frames at 14 fps, DivX format in an .avi container).
This is an example of one of the types of videos that FractVal can generate, Type II, the variant where the video features a fractal object whose palette is being rotated or altered in some way at a certain speed to generate a number of effects, such as ever-changing lighting and such. In this particular example a fractal tunnel undergoes fast rotating lighting.
For filesize and server space reasons this sample video has frames about 4 times smaller than the original I made and it runs at 16 fps instead of 25 fps, plus other size-related limitations which affect quality, but it will give you a fair idea of what's possible. Video details: 1.06 Mbytes, just 4 seconds long (blink and you'll miss it!), 640x384 frames at 16 fps, DivX format in an .avi container).
This is an example of one of the types of videos that FractVal can generate, Type III, the variant where the video features a fractal object which isn't static but actually evolves as the video goes on, it doesn't remain the same, it changes or moves on its own, it's alive ! (well, sort of).
In this particular example, you can watch a number of scattered sprouts in a hazy fog which quickly coalesces to evolve into a frog-like being, which continues evolving further into an octopus-like being that eventually separates into a big brain and a host of smaller bodies, with a hint of additional subdivision by the time the video ends.
For filesize and server space reasons this sample video has frames about 4 times smaller than the original I made, and it runs at 10 fps instead of 25 fps, plus other size-related limitations, but it will give you a nice idea of what's possible. Video details: 4.76 Mbytes, 40 seconds long, 640x480 frames at 10 fps, DivX format in an .avi container).
Another nice example of one of the types of videos that FractVal can generate, again a Type III where the fractal object itself isn't static but changes as the video goes on, it doesn't remain the same, as if it were alive.
In this particular Sample Video, titled "Unstable", you can watch a slowly-descending section of a fractal undergoing splitting and recombination while a stream of incandescent "lava" steadily flows upwards till it reaches the surface and burns everything on its way, turning black portions of the fractal into bright, curling smoke. And again remember, each frame is a static image which can be indefinitely zoomed, potentially having all the infinite detail of the fractal object it renders.
For filesize and server space reasons this sample video has frames about 2.5 times smaller than the original I made and runs at 15 fps instead of 25 fps, plus it's been heavily compressed but all the same it will give you a good idea of what's possible.
Old Egypt's Sacred Scarab. The resemblance is uncanny.
Bunker at Omaha Beach on D-Day, firing and being fired at.
Dad, Mom and three children merrily hanging around in the depths of the ocean.
Some nice silver jewelry, filigree style.
Notice both a Mandelbrot and a Mandelbar (aka Tricorn) visible at the same time in this picture.
A cosmic string travelling across the Universe at the speed of light.
Luxurious fractal jungle in daylight. Same geometry as VA255 but different color palette.
Luxurious fractal jungle at night. Same geometry as VA254 but different color palette.
These articles, programs, pictures, their descriptions and other materials created by me are (c) Valentin Albillo, and can be used freely for non-profit purposes as long as (1) the contents aren't modified in any way and (2) the copyright is acknowledged.
In plain words, you can download them and use them for non-profit purposes but do not include them in any media and/or site for which you're asking money, do not tamper with their contents and do not say or imply that you created them or that you don't know who created them, you must always give due credit to the copyright holder (that's me).