Remember the time you said you'd give me a dollar?

Okay, this one is definitely a Bennie. Although you'd have to zoom in a bit to see the minibrot in the middle.



In theory, this series should be worth an infinite amount of money, right?

Timelines and epicycles

Today's image is (a) directly stolen from the Spirograph instruction book I used to have, back in the day; (b) a companion piece to this one; (c) ludicrously slow to render.

A Modern Universe (for the City of the Future)



The pure-white background is disconcerting for me to look at. I rarely make anything so undiluted. But I wanted it to reflect the clean white sleek look of Modern design. All it needs is a bit of really geometric sans-serif type, a single word maybe, placed so as to provide the maximum amount of dynamic balance.

I very much want to make a big print of this one. The pattern-doubling repetitions around the minibrots are amazingly intricate, and would probably be worth examining more closely.

Alternating or direct currency

As a matter of fact, it probably is all about the Pentiums. Although I haven't been keeping track; there's probably some much better/cooler/geekier kind of processor available by now. Bah, and I can't even say this is a Benoit and call it a Bennie, because it's actually a Julia. Oh well.

Now that this is rendered, I'm wondering if it needs some kind of a border.

untitled [illegal tender]

Go faster!

I've done some further investigation of yesterday's excruciatingly slow fractal, and discovered that in setting it to render larger, it had indeed gone into arbitrary precision, which accounts for some of the slowness. I also figured out that I could switch to the associated Julia set and get an almost identical effect without having to zoom so deeply. So I've got a different version rendering now, and it says it has a mere three hours to go. Hooray!

Some tinkering with a nearby Mandelbrot region, and some nice quick simple orbit trap coloring, has given me an idea for a possible label design. I'm not sure about the color. It seems somewhat too dark.

Somewhat less than one pixel per second

I remember when I got my first computer, and I downloaded Fractint and would sit and watch as it rendered images, one slow line at a time. And I remember my early days of using Ultra Fractal, when new coloring methods would be written, some of them were ridiculously complicated and would render one slow line at a time.

Over the years, technology has advanced, processors have gotten faster, and I can open up some of those old parameters and have them appear in a few quick seconds. But somehow, I always still seem to end up staring at my monitor, transfixed, as an image appears one slow pixel at a time. Sometimes it's because I'm doing deep zooms, that get into arbitrary precision. Sometimes it's lots of layers. Sometimes it's ever-more elaborate coloring methods.

This tiny snippet is probably the slowest combination of things I've tried so far. It's a Mandelbrot zoom, with Extended Precision, fairly close to the boundary (so needing lots of iterations to avoid blank gaps), and with my own parametric coloring in a particularly slow configuration. At 400 x 400 pixels, this took four hours to render. I wanted to do a test of whether it would look like I expected, so as to be used in a larger, several-layered image. Unrendered, it dissolves into a mass of crunchy pixels.



So now I'm wondering, is it worth doing the somewhat larger render of the image that this is a component of? It looks like the guilloche-pattern effect is working the way it's supposed to. If I go by my on-screen working version, the colors and layers are okay. Render time estimate is somewhere between 850 and 900 hours. That's more than a month, assuming it doesn't slow down a lot when it gets near the minibrot in the middle.

Well, I've started it. It can mutter away in the background while I'm thinking of other things.

Image à trois

Whee, it's Friday the 13th! Pretty soon I'll be able to give this Valentine theme a rest. This one is only very loosely connected to it anyway.

Bizarre Love Triangle



It's a single-layer mandelbrot cubed. It turns out to be a lot harder to make bilaterally-symmetrical things (like hearts) when the geometry is pulling in three directions at once, so the little blobs aren't very heart-like. I liked the colors, though, and the way the three pairs spin out from the chaotic center.

Rainbows are also easy, unicorns less so

On the same general principles as my recent valentine-ish thing, another single-layer Mandelbrot zoom.

untitled [hearts mandala]



This one may get photo-etched and added to the series, or it may not. I haven't decided whether or not I want to explicitly include any imagery of the hearts-and-flowers variety. Is that what makes fractals so difficult to take seriously? That they're really good at making groovy flowers and rainbows and such? That once you dig deeply enough into the giant pile of numbers, you start finding cute?

And indeed, they are remarkably bad at conveying the kinds of social issues that are currently considered important. I would no doubt find it quite difficult to construct a fractal that would clearly convey the idea of "contested election" or "housing market crash" or even "walk/don't walk." Probably it could be done, but it would take some serious mangling, and maybe even something really unnatural like imported images. It would lack the simplicity of pattern that these one-layer zooms have.

Bah, I suppose there's more to it than that.

Buried under layers of gloom and cynicism

Things have been pretty grim around here lately, what with the weather and the economy and the beginnings of the worst final grind at school. But in the middle of all of it, I find that I'm making pictures with hearts in them. I don't quite know where that's coming from.

Several of them are deep-ish Mandelbrot zooms, which I have been finding interesting again. I seem to go through these spells where I want to go digging around in familiar places to see if anything new turns up, exploring the distortions of pattern around the minibrot molecules. So here's a simple, single-layer image, just a bit too early for February.

Valentine Rising

Quartz is the most common mineral in the crust

I just got home from a brief vacation in Montana, where I got to do a bit of hiking and admire the spectacular scenery and also dig in the ground in search of quartz crystals. I love the geometry of crystals, and I especially like the ones that are interestingly distorted or flawed.

There's always a sort of jarring transition when I've been out looking at natural phenomena for a while, and then look at fractals, and the fractals all of a sudden seem much too simple and perfect, and I despair of ever making anything that looks half as cool as the stuff that's outside. Over the years, I've tried to make fractal clouds, and fractal spectra, and fractal plants, and none of them is ever as good as the real kind. But they are, I suppose, interesting in their own way, and so I persist.

One of the kinds of crystals that can happen is called a scepter. (Some more nice scepter pictures here.) I only found one small example of this shape while I was digging, and sadly it was full of internal fractures, so much so that it started to break apart while I attempted to brush sand off it. But the name made me think of a silly pun, so I came home and made a picture to go with it. So, from the mountains of Montana, and the Scepter Valley of the Mandelbrot set:

Amethyst Scepter

These primitive tools

This one is somewhat related to the previous couple, but ended up brighter. I could probably have given it a nice cheerful, sunny title, but I'm still in Intrepid Explorer mode, so it's called

Bronze Axes



(There are two axes, the real axis and the imaginary axis. Ha ha. I'm an idiot.)

Hooray for Captain Spaulding

Just when I think I'm completely jaded and done with fractals, things come along and give me another nudge. I was looking at the ever-reliable Fractal Complaints Department, and although there's never actually anything new there, it did remind me that it's been a while since I made any brightly-colored, excessively-layered spirals. So tonight I spent a little time exploring.

Into the Jungle



While wandering through these shadowy (though remarkably well-charted) regions, I found myself surrounded on all sides by the usual sorts of creatures: things with spines and scales and multicolored warts and, of course, lots of spirals.

Pathological Monsters



These two are both Mandelbrot zooms, with similar locations and many of the same coloring algorithms applied. I have a few others saved; maybe at some point I'll post more and call it a series.

Orbiting thingummies

This one is for the Professor, and also for the new curtains.

Atomische



A z³ mandelbrot, seven layers.

A self-portrait of sorts

After this, I think I'd like to go back to more abstract things for a while, and stop trying to make the fractals look so much like something specific.

Where Does All the Wasted Time Go?



This is a Mandelbrot image, of course. But it's six layers, instead of just a single-layer zoom, so it's slow enough that rendering it took about three days.

Bling

I'm actually pretty happy with how this one turned out. The colors worked well, for a single-layer image.

Blue Diamonds



Magnification 1.8161869x10³⁵. It took a stupid amount of deep-zooming to get the diamonds to be even slightly the right shape, and thus the render was probably the slowest of the whole bunch.

I made some Purple Horseshoes, but they looked only slightly like horseshoes, and a lot more like the cross-section of some mutant purple celery, so I probably won't post them.

I fear my luck is running out

I'm not even to the end of the week, and already I'm really sick of this series. This one is better than the hearts, at least.

Green Clovers



Magnification 5.463162x10¹⁷. I had to crank the maximum iterations way up on this one, which made it render excruciatingly slowly.

100% pure cheese

Continuing my series of single-layer mandelbrot zooms: a minimalist sort of image, with stylized rays and the sun in the middle.

Yellow Moons



Magnification 2.6467484x10¹⁵. A nice quick render.

Don't thank them yet

Second in the series of single-layer Mandelbrot zooms.

Orange Stars



Magnification 4.8710492x10²⁵. The spirally stuff in between them is meant to be suggestive of nebulas or space dust or some such.

Serial molecules

One of the well-known properties of the Mandelbrot set is that it's full of smaller, distorted copies of itself. I've just found out that Mandelbrot himself refers to these as "molecules," which I think is a wonderful name for them.

Over the last week or so, I've been doing a lot of systematic exploring of the Mandelbrot, trying to get a better feel for the patterns around the molecules, and how those patterns are affected when you zoom into different sub-regions of them. It's fascinating; they distort in all sorts of ways, and I'm getting better at predicting and working with the distortion to find the shapes I want.

I must confess, though, that so far the results have been embarrassingly silly. This week I plan to post a series of single-layer Mandelbrot zooms, the reaction to which will probably be the same hollow groan that follows a really bad pun. To begin with, the image that started me on this exploring binge in the first place.

Pink Hearts



The magnification is 2.3422469x10²⁰. I've surrounded them with thorns, because it seemed suitably poetic, or symbolic, or something.

Hypocycloid with chromatic aberration

This one is from March or so, in answer to a question which wasn't actually directed at me.

Because They Don't Understand



It's a Mandelbrot, it's at least five layers, and that's all I can remember right now. I'll have to dig out the parameter file at some point, to see if there's anything particularly noteworthy about it.