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Tag Archives: Mandelbrot set

G’day. During the last few weeks, I’ve been using FD and exploring regions of the Mandelbrot set I’ve not before seen, simply because I hadn’t looked! These images are from generalizations carried to higher exponents of Benoit’s discovery, and so I thought to revisit his classic set, where z is carried to the 3rd, power, the 4th power, and higher still. Of course this may have some effect on calculation speed for the app, especially when zooming in ever deeper, revealing ever more hidden landscapes, perhaps some of these unseen by human eyes? I won’t presume to answer that – I can only say, “I don’t know,” and that’s perfectly fine.

Here are three 2000 x 1000 pixel images that may help to inform that question, at least a little…




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 2014 by Troy Loy.

G’day. There’s been work done on FD with Julia sets lately, employing the complex plane coordinates of [C -0.835 ; + -0.2321] used to generate all of the following images via a Mandelbrot set (Essentially a map of Julia sets where each point on the complex plane has its own unique Julia set associated with it).

Julia sets generated in this manner have a sort of exact self-similarity, and some areas of the figure tend to look much the same at any scale, so creative use of parameter settings is recommended when generating these!

This particular set of images strikes me as kind of odd-looking, perhaps dragonish in shape, but employ the simple maths used to generate them in ways that take full advantage of the variations possible even with the same basic formula and seed coordinates.

Have a happy Thor’s Day!

Wyrm of Spines

Wyrm of Spines



Aspect Null

Aspect Null

All JPEG, PNG & GIF images in this post are original works by the author,created by

way of XaoS, Mandelbulber or Fractal Domains, and are copyright 2013 by Troy Loy.

Here are a few images that I came up with over the past week, all of them Julia sets, some from a Mandelbrot set, and others from Newton or Halley method images, but all having a common theme: the recurrence of a winglike, feathery structure and an odd luminescence about them, or metallic gleam reflecting strange light sources like alien suns. I’ve sought to vary the ways they show these traits, and excluded images that differ only in their color maps. These images are as yet untitled. Suggestions are welcome!

All JPEG, PNG & GIF images in this post are original works by the author,created by

way of XaoS, Mandelbulber or Fractal Domains, and are copyright 2013 by Troy Loy.



I started my hobby of generating fractals, beginning with Fractal Domains, then XaoS and Mandelbulber, as a way of creating my own copyright-free artwork for this blog. I got tired of using other peoples’ work, even with permission or when in the public domain. But as many of you probably have noticed, it quickly snowballed out of control into the horrific monstrosity it is today.

I rather like making these silly things, and they’re a useful outlet for my frustration, dark moods, and fits of awe alike.

Over time, I’ve come up with a set of useful guidelines, rules-of-thumb, or what-have-you that I’ve found handy for effectively and consistently coming up with images that even when not pretty to look at (Sometimes, pretty is bad. Dark and creepy, surreal, and even erotic have their place too.) can spark people to see totally different things in the same piece.

Such is the power of the human imagination when seeing weird imagery.

Here are a few, pending my noting yet more of them or amending these in future posts, and none of these being set in stone.

  • Learn the app, whether by trial-and-error, reading and practicing from the manual, and anywhere between these. This should be a no-brainer, but getting overconfident with a new app without familiarity with the software lessens the quality and range of the images you can produce. If nothing else, experimenting is useful in finding out which settings have what results in the final images. Some apps have a more limited range of types of images they can produce, but knowing the software maximizes the variety and awesomeness of the work generated.
  • As briefly mentioned above, experiment, and often. Never be afraid to ask yourself, “what happens if I click on this button, or type this number into an input window?” Even if you mess up, with most apps I’ve seen you can reset to default mode or otherwise undo the results, and experimentation shows you firsthand what NOT to do. Be careful with some apps, though, and at least glance over the manual to know what combinations of settings will really hurt image quality or unnecessarily slow down rendering, often to a crawl when you must budget your time. Some programs will allow you to preview the results before rendering, so you may nix poor results and try again before unwittingly giving your CPU fits or making your media viewer very cross with you.
  • When you can, shift between apps periodically. Sometimes, one can get into a rut only using a single program for long periods of time, so it pays to have more than one app available on your system. Give yourself a break from using one program and switch to another to try out any ideas that come for potentially cool images with that, or even for exploration’s own sake. Taking a break from one app and switching to another temporarily gives you time to go back to the former later, and look toward image creation again with fresh eyes and a fresh mind, though hopefully not a cheeky one…
  • Try to avoid using the same set of parameters more than, say, two or three times unless you are making a commissioned replica of an image, or a particularly striking version of it at a different pixel-size. Whenever possible, never repeat color combinations for an image. Always try to move out of a comfort spot that may develop when you find things looking and feeling too much the same. If you don’t, others will. The goal is to keep the images interesting and novel, not just to duplicate earlier work, again, unless it’s a commissioned piece or for a specific purpose like rendering thumbnails of larger images, murals, or poster prints.

Hopefully, others will find these as useful, though no set of normative standards is ever completely definitive. But I’ve found them very helpful, and though they’re not logically self-justifying they work, at least for the present. Try your hand at making your own images, and good fractaling!


This week, I’m mixing images from different apps in one post. The top image was done using Fractal Domains, using a modified Newtonian or Halley method formula, the shapes produced by trapping the geometric orbits of the number set, and the color map was randomized and selected for in an almost Darwinian fashion, but artificially, not naturally.

The lower image may make some of you a bit queasy from the resemblance to diseased tissue or to me, something out of Lovecraft, but it’s a closer match than the above to what I’ve termed ‘horrific elegance,’ with it’s non-euclidean, alien-looking geometry giving sometimes monstrous results.

Maybe it could be something that Cthulhu’s interior decorator would come up with. This image was generated via Mandelbulber, using a customized parameter set, I believe a power-6 3D Mandelbrot set.

It’s hard to believe that such images were produced using a piece of hardware built with silicon chips employing mathematically precise software commands and formulas. But that’s science behind it all, both quantum electrodynamics, computer engineering, and the maths of fractal geometry.

 Images copyright 2012 Troy Loy


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