Spiral Galactic Megacluster Cloud Discovered
Announcing: the find of a cloud currently giving birth to a megacluster of spiral galaxies. Also known as my gift to Apophysis for incoming 2012, and a way of saying "thank you" to its developers for this amazing programme.
This began in 2004, when I was exploring how to make the Blancmange Curve fractal (BMC) in the Brazil IFS programme. I succeeded with the BMC easily enough, and then began experimenting with alternate versions, branching out. One such alternate was the addition of a "spiralizer" holon 1/sqrt2 in size (c. 0.707), rotated 45 degrees clockwise. This produced a nice spiral, so I tried the same extra holon with other IFS fractals which I had already made. More great spirals, more experimenting.
Eventually I realized that there was a *huge* set of spirals to discover, all based on 2 or 3 holons of 0.5 size (squares or 45/135 degree parallelograms) and the one "spiralizing" holon, the 1/sqrt2 one rotated +45 degrees. This one, too had other variations: -45 degrees of rotation, a flip, etc.
Starting out with a basic set of holons, I began making variations on these; this time using the Copy, Find and Replace functions in Notepad to speed things up greatly. Some of the sets of 0.5 holons, without their spiralizer, produced classical fractals such as the Dragon Curve or Levy's Curve; others led to a single line, or even to dust. No matter - add the spiralizer and everything changed.
The result is 3 sets each of 38400 spirals and variations, all labelled the "BMC Spirals" in honour of their starting point. I have broken the whole thing into smaller sets to as not to overwhelm Apophysis with one gigantic file. A caveat - there may be as many as 1% duplicates; I have not yet even rendered the whole set once. These are but keyframes, however, for a literally infinite set of animation frames - from any one spiral to any other, and so on...
The relationship between items with the same number is that only their spiralizers differ. The unlettered set, 38400, are the original, "standard" versions. Letter "a" have the most spectacular variations; "b" are less spectacular but still noteworthy as spirals.
Apophysis, however, seems incapable of rendering these spirals in the same standard size that Brazil or Fractint do, either filling a unit square or occupying a precise fraction of it from corner to corner, such as 1/2 or 1/4. One must establish a size and position for each spiral, which is not necessary to do in either of the above mentioned IFS programmes.
The other non-standard thing is the "intensity" of the spirals, which varies from one to the next and must be determined aesthetically by the user. This is due to varying amounts of "concentration" of the holons' output, from strong (much of the spiral lying on top of itself: high natural contrast) to weak (much more spread-out appearance of the spiral: low natural contrast). Once a fairly standard intensity for each spiral is determined, however, use of the spirals as animation keyframes will give much more pleasing results than if this is not done. There may be a mathematical process discoverable which will result in a small range of intensities for the whole set of spirals, and this too would speed up results greatly.
I've included here links to:
1) a sample file to show some parameters of favourite spirals I've found. But, of course, with 38400 x 3 of them to look at, each person will have other favourites: https://docs.google.com/open?id=0B2loyA ... JiNDU3NGI5
2) the whole set of BMC Spirals, ifs format, zipped: https://docs.google.com/open?id=0B2loyA ... lhM2ZlYmFm
Tbilisi, Republic of Georgia