Logico Fractatus | Halley’s Method: Pitchfork Infinity

Vanakkam. Here’s a recent image, created using a Halley Julia set and some really cool pseudo-3D effects via Ultra Fractal 6. I’ll be using the original PNG file to make poster prints on my DeviantART account. I dislike how this one turned out less than I might. I grant it a stay of execution…this day!

Tf. Tk. Tts.

Logico Fractatus | Quoted in Character: Inaugural Post

Vanakkam. Today, I begin a series of entries involving quotes from my fictional characters who, using their own perspectives in the Gods of Terra setting, capture something of modern scientific skepticism. Future installments get their own title, but since this one uses a recent image, it piggybacks on Logico Fractatus. The image I used for this is a Julia set of the Burning Ship fractal type , via Ultra Fractal 6. Today’s quote comes from one of my oldest Gods of Terra characters, Dasaelos Gurao, Warlord of the Rj’lt’ar species.

Tf. Tk. Tts.

All JPEG, PNG, Tiff, & GIF images in this post are original works by the author, created by way of various fractal apps, and these are copyright 2019 by Troy David Loy unless stated otherwise. 

Feel free to save or distribute these images for private, noncommercial use, or elsewhere online with a link to the original source and/or credit to the author.

Thank you!

Logico Fractatus | “I Shall Call It — Mini-Mandelbrot.”

Vanakkam. Today’s image is courtesy of Frax Pro, here a deep zoom of a border region along the valley of the Mandelbrot set’s main cardioid, the heart-shaped area of the figure located in quadrants one and four on the complex plane. I found this one worth keeping in my files, as I dislike it less than some others generated in the same batch of images. Others shall be relegated to my Bad Fractals folder, or condemned to permanent status as mere gradient maps for coloring better looking images. I’m releasing this piece into the public domain.

Tf. Tk. Tts.


Logico Fractatus | Here There Be Fractals #001

Here’s my first fractal slide show video. I own the copyrights to the images, and the music is my own, created via GarageBand. Video editing and composition is via iMovie. No Maine Coon cats or fractal dust mastodons were harmed in the making of this video.

Logico Fractatus | Valentine’s Day, 2018

To my readership, friends, and family: Ricky the cat and I wish a happy Valentine’s Day to all who celebrate it.

Logico Fractatus | Bad Fractals – Part 2

G’day, O fine humans! For this installment, I’ve another Bad Fractal, with its less-than-awful twin following. I’ll first show what’s wrong with the image, then tell you how I fixed it in the second take . . . .

This one looks innocent enough, but here, note the tiny silvery dot at the origin point, right at the center of the picture. I’ve used orbit traps with both of these pictures, but in the image above, they are too small, and the very largest of them can barely be seen, while the others are invisible! While the color mapping (the algorithm that assigns a color to each point in the image) is not that bad, the pseudo-3D effect of the orbit traps is useless and mars the image. So . . .

. . . With this one, I magnified the orbit traps up to 500 times the base size, and chose circular traps with just the right coloration to look like an eyeball with jointed tentacles. I’ve left the exterior regions unchanged, at least in this version. In Fractal Domains, the app I used for these, the circle and square orbit traps are the smallest for some shapes, and often require being scaled up much more drastically than stalk orbit traps based on real or imaginary number coordinates, those points on the complex number plane used to render the fractals. I’ve also reduced the number of colors available, keeping the image from being too busy or blurring into each other and spoiling the lines of the image!

So, I’ll be back soon with more Bad Fractals and their less-awful mirror-universe counterparts, and until then,

Tf. Tk. Tts.

The images shown in this post are, unless otherwise stated, the personal creations of the author, and unless specified to the contrary, are copyright ©2017 by Troy David Loy, AKA Troythulu. You are free to use the images here in any non-commercial way on your own venue(s), as long as you credit the source or post a link to that source online. Thank You!

Logico Fractatus | Bad Fractals – Part 1

For a couple of months now, I’ve been involved in the work of deliberately creating some pretty Bad Fractals, as I call the project. Here, the goal, which is turning out swimmingly, is to find those “10000” solutions that won’t work,” to find and better by far those solutions, techniques, tricks, and tips that do to make better images. Here I have three images, two Bad, progressively less so, before reaching the third, and final image of the set. So, I’ll comment on each, and discuss what I like and don’t like about it, and why I think the Bad Fractals are just that. The images below are all courtesy of Fractal Domains for Mac. Let’s start with the first, and the worst of these! This post’s images use a modified Newton’s Method fractal type, and I’ve added terms to the formula’s numerator with higher exponent values. Bad Fractals in this series use 800 x 450 pixel resolution unless otherwise indicated:

I have serious problems with this one. While the pixelation with this could be corrected, the real issue here is the color maps used, both in the orbit traps and the fixed points. In short, this one’s colors are far too busy. In the orbit traps they bleed into each other and spoil the image’s detail, blurring the definition of the orbit traps and so spoiling the esthetics of the piece. The fixed points outside the orbit traps are too garish for my tastes. I attempt to fix those issues with the image just below, but even this has problems . . . .

This one is a bit worrisome too, even with the color maps adjusted. One, the color map of the fixed points clashes with that of the orbit traps, and two, the orbit traps are split by the orbits of the fractal set, which means I have to define the color map for each orbit region. I have improved things a bit here by lowering the range of colors available for color randomization, my usual method before adjusting color maps manually, so what appears immediately above isn’t that busy. Still, even with a reduced range of colors involved, the mismatch between the earthy shades of the fixed points and the more floral-looking orbit traps becomes apparent. So let’s try for something that doesn’t clash so much:

This one is a reasonably full-sized 1600 x 900 wallpaper, so the pixelation isn’t nearly as problematic. I’ve finally got the image to something a bit less Bad, just a wee bit, because I fixed the color map problems and the orbit trap settings of the previous two. This one had a maximum color map selection by use of randomizing somewhere between 9 and 12, and a minimum of 2, and this greatly improved the colors of the first. This one is much better even than the second in that there was no region-splitting for the orbit traps with the colors I got, so those don’t look out of place with the maps for the fixed points. The colors for traps and points fit much better together here, as I took more time selecting a better match for each. I think that this one seems a better image as a result, but you be the judge using your own sense of taste, not mine!

Tf. Tk. Tts.

The images shown in this post are, unless otherwise stated, the personal creations of the author, and unless specified to the contrary, are copyright ©2017 by Troy David Loy, AKA Troythulu. You are free to use the images here in any non-commercial way on your own venue(s), as long as you credit the source or post a link to that source online. Thank You!