Logico Fractatus | Indra’s Spirals [1]


Today’s piece is something I created on Ultra Fractal 6 using the Indra’s Promise formula, and a multi-layered mix of its sub-formulas and color gradients. I’m working on a Halloween-themed image for later this month, so until then or the next post, whichever comes first ….

Tf. Tk. Tts.

Fractals of the Week | 2016.09.07


Screen Shot 2016-08-11 at 17.12.20

Talotaa frang (be well!). This week, I present some wallpapers via UltraFractal 5, two of them with an embossed look, as I explore the app’s flexibility with that sort of image. There seems to be a compatibility mismatch between certain formulas and the embossing coloring algorithm, so it’s not going to work for all. I’m in the process of learning more about the code the formulas are written in to expand, through custom presets, the variety of interesting fractal types that may be used. This will be combined with a more thorough look at the formulas and options possible for them, to expand my sample size when it comes to knowing what code of what formulas permit embossing. One thing is a definite improvement over XaoS embossed fractals, and that’s the shading and color that’s possible through UltraFractal.

So here’s a sample of that.

UP5_25D

This has a curious, almost spiky quality to it, centering on a mini-Mandelbrot set, almost like a spider at the center of its web. This was a deep zoom, with a slight incompatibility to the coloring algorithm, that apparently did not significantly hurt the image.

UP5_26D

This was a normal, non-embossed fractal, using a rings-and-loops coloring algorithm, that I nonetheless had fun with. My favorite is for last…

UP5_25K

 This uses a Newton fractal type with embossing, and here I’ve adjusted the shading angle sightly for effect.

These images are all 1600×900 pixels in size, so click to humoungify for full size.

Tf. Tk. Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

Fractals of the Week | I’ve Got Newton on ‘Dis!


Screen Shot 2016-08-11 at 17.12.20

This week, I feature images using the math of a certain cranky English guy, responsible for the Laws of Motion, and those Harry Potter-esque alchemical experiments in his attic, trying to convert base metals into gold, and create the Sorcerer’s, er, I mean Philosopher’s Stone. These pieces, a couple released for the first time on this blog, also use symmetry transformations, or mapping, from a range of mathematicians, including one (#2) whose work has been featured before, Felix Klein. Regardless of their origination, these were fun to play with, and will be followed by more in future.

UF5_23

UF5_21C

UF5_22F

Each of the full-sized images measures 1600×900 pixels, so feel free to double-click for complete ginormification.

Tf. Tk. Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

Fractals of the Week | Newtonmas 2015 – On the Shoulders of Giants


Screen Shot 2015-11-27 at 13.38.40

This post marks, only shy of by three days, when this blog was begun on December 28th, 2008, and it marks as well the birthday of scientific giant Isaac Newton in 1642, whose discoveries brought on the age of industry and the scientific revolution, changing the world forever.

So, here are a set of images using the very mathematical technique that he developed along with contributions from Joseph Raphson and others, for finding the zeroes or roots of of functions using real numbers applied to fractals.

May you all have a wonderful winter solstice holiday, however you celebrate it or whatever you call it, with a most pleasant and awesomositous new year. Double click to enlarge these.

Newton_3

Newton_6

Newton_4

Newton_8

Newton_7_Hilbert_Curve

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2015 by Troy Loy. I hereby permit the free, noncommercial use of these images, as long as proper credit is given for them.

Fractals of the Week | Indra’s Sky (full of Moons!)


G’day! This week, I present a new Kleinian group image, this one completed just yesterday. It uses a three-layer multicolored rendering with a mapping that gives the look of a reflective lake in the foreground, a lake where spiral patterns of moons rise above the horizon. The maths for this one are found in the book Indra’s Pearls: The Vision of Felix Klein, which I highly recommend even for those with only basic proficiency with algebra. The image is directly uploaded to WP, so double-click to enlarginate for the full-sized file.

Tf. Tk. Tts.

A Sky Full of Moons

A Sky Full of Moons

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2015 by Troy Loy. I hereby permit the free, noncommercial use of these images, as long as proper credit is given for them.

Fractals of the Week | Indra’s Fire


G’day! This week, I start on a new project for this series, a set of Kleinian group images based on the math in the book Indra’s Pearls, with some new tricks I’ve discovered in fooling with UF5. These two images have been uploaded to deviantART, each linked to its page, and are available as free downloads and as printed wall-hangings. At 7200 x 7200 pixels, these are enormous files, and I’d advise caution for your device’s sake if and when downloading them. I’ll explore Kleinian groups in ways I’ve never done before. Let’s see what alien nightmares may come of this…

TfTkTts.

Indra’s Goblet

Agnium

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2015 by Troy Loy. I hereby permit the free, noncommercial use of these images, as long as proper credit is given for them.

Fractals of the Week: Testing the Limit (Sets)…


I’ve created a few more thumbnails from limit sets, by adding a bit of chaotic behavior to the mix. Here are some of those, with their spiral curves, never quite touching but cool nonetheless. I’ll test out direct manipulation of parts of the code via the compiler built into the software to see what I get, for much larger pieces worth printing as wall hangings.

A confession: Last month’s project image had suffered from misaligned tiles when positioning, so, like the elf I should have been, I scrapped the image and started again from scratch. So far, at 69 tiles out of 240, there aren’t any of them out of place or overlapping with the others this time, and image clarity is good.

This is a good sign.

I’ll post a link to the finished piece when it’s uploaded to deviantART, but doing so in haste is bad ju-ju. That’s what brought me trouble with the first try. The finished piece will be 18000 x 10800 pixels at 300 dpi, or fully printed at 5×3 ft in size. I think that’s worth taking time on. So, here are more products of my diabolically vile experimentation…

Talotaa frang.

LimitSets_11

LimitSets_9

LimitSets_10

All JPEG, PNG & GIF images in this post are original works by the author, created via Mandelbulber, Fractal Domains, Ultra Fractal , Frax, and Mandelbulb 3D and unless otherwise stated are copyright 2015 by Troy Loy.