Friday, June 17, 2011

Fractal eXtreme: The NovaM Set

I cannot begin to tell you how awesome this fractal set is... "The possibilities are infinite", as they say on Fractal Forums, and in the case of NovaM, this is truly the case. As with all the other sets I've shown you since the original Mandelbrot, I won't go into the maths of this one because honestly, even though I am more than capable of understanding it all if I wanted to, I'm just too fascinated with the colourful results to care. From what I remember from reading about it though, I can tell you that it is based on the Newton Set formula, but it adds a constant (either a real or complex number) after each iteration. This constant is what Fractal eXtreme allows you to vary, through the Plug-in Setup option.

And not only does it have that variable constant, it also has a Julia form... Are you starting to imagine what possibilities we have here? Well I'm gonna show you. First, take a look at the fascinating creature that loads as the NovaM default:

NovaM x: 3

Isn't it gorgeous? As the caption states, if you go have a look at its Plug-in Setup, you'll find x is 3, and y, 0.

From here, you have a multitude of options. You could simply start zooming in. Or, using Plug-in Setup, you could start changing that x value. (Or the y value, or both!) Just with this feature alone you can yield thousands of amazing Fractals to explore, yet it's only the beginning... For every change you make to those x and y values, you are able to generate an array of Julias and of course you're able to zoom into those as well(!).

Do you see how I spent hours playing with this Set last night?

[Oh, something you should know: Because of the immense complexity of this Set, the image takes longer than most to render, especially as the x and/or y values get higher and lower. A minor issue, considering the extraordinary results that can be achieved. Still, I'm looking into what I can do in terms of hardware, to make my fractal software faster. Will be especially necessary when I really get down and dirty with 3D fractals.]

[Another issue: Even if you have the full version of Fractal eXtreme, this set has a zoom limit. Sometimes this is really frustrating, like just before you reach that deeply nested Mandelbrot that you KNEW was there :P ... Still, what IS possible is already closer to the infinite than not. I'll make it my mission to find all the best Fractal software soon, and report back with a software section on the site.]

But ok, so let me show you all the possibilities... First, here are 8 (I couldn't help myself!) examples of what you can find if you simply zoom into the default NovaM (with x=3). As you can see, the first four are of Mandelbrot shapes (they occur everywhere) while the last four are more abstract:

The next thing I decided to do was generate a few Julias, still using only the default NovaM. Remember that a Julia exists for every point on the complex plane. So using the alt-click function in Fractal eXtreme, you can "warp" the Julia until you find one you like. Here are three such examples, each with a respective zoom-in:

NovaM Julia x: 0.306 | y: 0.239
Julia x: 0.306 | y: 0.239 ZOOM

NovaM Julia x: -0.531| y: 0
Julia x: -0.531| y: 0 ZOOM

NovaM Julia x: -0.584 | y: -0.044
Julia x: -0.584 | y: -0.044 ZOOM

Next, I played around with the x value. The default is 3. I slid it down a bit and found you could still find interesting zooms up until about 1.5.  So nothing interesting between 1.5 and 0.

NovaM x: 2.25
NovaM x: 2.25 ZOOM
NovaM x: 1.5 ZOOM
NovaM x: 1.5

From about 0.250 you have a rainbow "bean" that keeps getting smaller as you approach zero. Zero is just a big blank blue screen. But at -0.001, the bean pops back into view and gets smaller still. I zoomed into it and found nothing but streaming rainbow colours. Besides getting smaller, it stays like this until you reach -2.000, when the bean's node explodes outward, giving shape to some peculiar fractals, as well as little fractal germ-like creatures orbiting their bean-planet :) So zooming in between -2 and -8 can be quite interesting.

NovaM x: -2.1
NovaM x: -2.1 ZOOM

NovaM x: 3.85
NovaM x: 3.85 ZOOM

Actually, after -8, is doesn't really look like there's anything worth looking at, but just to test, I went to -38 and zoomed in at the "node". The top image is what the bean looks like (more of a circle now) and below it is an example of what you can find if you zoom in deep:

Nova x: -38.85
Nova x: -38.85 ZOOM
Now it's time to check out x values higher than 3. You'll see they produce even more amazing results than below 3. From 3 until about 12, the change to the fractal is dramatic, but after 12 it seems to just repeat the number of colour-beams and the dark circular area gets larger and eventually folds in on itself, all the while getting slower and slower to render. But for curiosity's sake once again, I checked out x=38 and found that when zooming deep enough, and having patience for the render, one can still find worthy fractal material. Here are two good examples, with two different Julias each, as well the x:38 experiment with a zoom:

NovaM x: 5.8

NovaMx5.8 | Julia x: -0.669 y: -0.051
NovaMx5.8 | Julia x: 0.006 y: -0.219

NovaM x: 12

NovaMx12 | Julia x: -0.057 y: -0.064
NovaMx12 | Julia x: -0.669 y: -0.051

NovaM x: 38.5 ZOOM
NovaM x: 38.5

I could have added so much more... Zooming into the above NovaM's and their Julias produce astounding results... But this blog entry is getting a bit long. If you're anything like me though, you've already gotten lost in zooms after entering the x and y values yourself :)

Now, lastly, we have come to what happens when you change the y value as well. I'll simply post a whole lot of examples with the values in the captions, and leave the rest to you. I hope you've liked this entry as much as I've enjoyed making it... So much infinite, beautiful complexity yet to explore!

NovaM x: 1.25 | y: 1.95
NovaM x: 1.95 | y: 1.65
NovaM x: 3 | y: 1.6
NovaM x: 3 | y: -3.4
NovaM x: 3 | y: -6.6
NovaM x: 3 | y: 7.95
NovaM x: 4.8 y: -2.25
NovaM x: 5.2 | y: -1.25
NovaM x: 7.85 | y: -1.5
NovaM x: 0.1 | y: -1.8
NovaM x: -0.65 | y: 6.9
NovaM x: -7 | y: -3.3
NovaM x: 21 | y: -6.35

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