search 2013 adfgs

Posts Tagged Mandelbrot

2 more!

While watching the stats for the last year, I noticed there were much less posts than I wanted or could have made. This will change. Here are 2 more images from the all-formula project. All the images are named after the formula that originated the fractal, and I will be telling when the formula is from a new formula collection if needed, maybe not. I guess letting too many guesses about how they are made makes the game not as funny. Click the image to see them larger as usual.

Chaosbrot Mandelbrot

Chaosbrot Mandelbrot

Hyperbon

Hyperbon

 

Related Images:

Tags: , , , , , , , ,

Fractals: photography or painting?

I was thinking other day… and suddenly this clearly came to my thoughts: fractals are more like photographs than paintings. I’ll try to explain why I think that way.

Fractal images, besides a lot of different interpretations and meanings, are nothing but graphical representations of a certain formula. Pretty much like that algebra class you had in high school. Although it can be artistic and all that (despite some refuse to call fractal art an art but this is another subject), it doesn’t even start (sometimes) with a blank canvas like a painting. You don’t create anything fractal-ish in the sense of inventing it. These graphical representations were all there already.

Algebra

Yes, a fractal is pretty much like that.

Take any fractal formula, say for example the Mandelbrot. It has a few parameters, but let reduce them to 2, X and Y for the sake of better understanding. The resulting image of the combination of the values of parameters X and Y gives you a certain image, the graphical representation of the combination of these parameters. This combination always existed. It was just waiting for someone to “create” the fractal with these values in a fractal generator software and publish it as a JPEG. Pretty much like the picture of a landscape, for example. The landscape was always there, waiting to have its photo taken.

What is a photograph if not a graphical representation of a landscape or a particular object in a specific moment in time, in a certain (constant, sometimes) environment? Take a picture of a mountain. Then the next day, the mountain will still be there, at the same place, in the same coordinates/parameters. If you go there and place your camera in the same position, with the same conditions (parameters) as when you did a day before, chances are that you will get the same or a very close image to the previous image. This is even more correct if you’re taking for example a picture of say a fruit in a studio. You can move your camera a few milimeters away from the original point of the first photo, and it’s about the same as using let’s say values of 0.000001 and 0.000002 for a certain parameter in a fractal. They are “pictures” of a fractal taken in a different condition, but they still keep the same basic subject, the fractal “structure” so to speak, just like the mountain or the car or the apple is the same.

And what about the post-processing? If you take a picture of a model in a studio with a red light today and tomorrow you use the same model, in the same position, but with a green light… it’s the same as using a different color algorithm in a fractal.

A painting is a bit different, because it’s your own interpretation of something, it’s not something that “is there” waiting to be unravelled. Each artist has a different technique and a way to “translate” things to a painting in his own way, some like to make the paintings entirely abstract, some like to make accurate reproductions making it look like a photograph, and although people can add their “personal touches” to fractals, these are more like a camera lens or some other dark room effect added to the image than a real “personal” touch. But this doesn’t mean that fractal artists aren’t creative. I hope I could make myself clear.

The trick I guess is to find the “right side of the mountain”, the correct time of the day to take your picture. The same landscape might look boring today and tomorrow with a few natural “tweaks” (a word constantly used by fractal artists) it can become a masterpiece. Sometimes it’s a matter of luck, sometimes you have some inner voice telling you to explore a new combination/spot, whatever. What is important is what you can do with that – the final work.

Related Images:

Tags: , , , , , , , , , , , , , , , , , , , , ,

A Mandelbulb for mr. Mandelbrot

Silly, ugly, whatever, It doesn’t even have a watermark.

For Benoit Mandelbrot

Benoit in the jungle

Related Images:

Tags: , , , , , , , , ,

R.I.P. Mr. Mandelbrot

Due to some personal issues I just got the sad news 5 mins ago. R.I.P. Master Mandelbrot. See you soon. Here’s my humble tribute. There’s not much left to say but a huge THANK YOU.

Thanks, mr. Mandelbrot.

A sad tribute to a very important man

Related Images:

Tags: , , ,

Some more on fractal movies

I’ve moved the animation that I had saved to a faster computer, but it refused to render, it wasn’t rendering even the very first frame. Time to think a little why it was happening. Maybe some folder permission error, not really a software bug.

In Mandelbulb 3D, in the animation window, you have the option to send back the saved keyframes to the main window (useless feature? Not at all!), so this is what I did. Sent them back, re-rendered each and send them back to the animation timeline, and saved this animation under a new name and in a different folder just to be sure. And it worked.

It’s currently rendering right now with a couple more frames added towards the end of the previous version (but I’ve reduced the number of frames between keyframes from 50 to 25 to see what happens, therefore the movie should be shorter this time) and 150 frames out of a total of 250 are already finished in 18 minutes. Quite an improvement. I think that I can even raise the size of the animations to some sort of “semi-HD” quality. I’ll have to check first if these fractals used here are also faster than others, sometimes when adding a Julia calculation or a “Cutting” things get a bit slower. Anyway, this is much much faster than rendering it in the other computer, that has half of the memory of this one, but the processor is a Celeron while in this other one it’s a quadcore… it’s not RAM that makes the difference here, but the processor. And maybe the video card (I have a Radeon something in the faster computer), but I’m not sure as it doesn’t really help in other softwares like Ultra Fractal to have a faster video card, these cards are more useful with games and… well, 3D processing. Definitely fractals aren’t for slow computers.

One thing that I’ve noticed though even in the preview animation window is that for some reason (or maybe it’s not really happening) is that the keyframes I had already used and all the frames inbetween these are rendered a bit faster than the new added keyframes. Sometimes deeper zooms render a bit slower too, this might be what’s happening as it’s a little deeper in these new frames.

Another thing I’ve noticed that seems to happen at least in this image is that in areas that have a certain depth of field, showing parts of the “sky” (or of a background image), the render gets much slower. The more sky/background, the slower it gets. If the image is filled with just the fractal parts, it goes much faster. The elements that are closer to the camera for example, are rendered much faster in an image that has “sky” parts even though they look much more complex than the plain blue sky behind them. I guess it’s due to the 3D, it has to calculate the distances from for example the border of the fractal to the “horizon” or the “sky”, which is quite far from the camera (I guess this calculation is limited by the iterations as well, it tells the software where the “sky” – the end of the image – is). The difference is brutal. Frames with about 30-40% of “sky” areas can take up to 20 mins to be rendered, maybe more (just one frame!), while others with minimal open areas are rendered in 40 seconds. So a good tip for a fractal animation using Mandelbrot 3D is… avoid these open areas, focus on the fractal details. Which is the most interesting part anyway.

Update: it is really getting slower. Last frames past the #200 are taking 7 mins to be rendered and it’s getting considerably slower from there. Maybe it’s really the zoom, the frame #207 for example has a zoom of 1599946.7something while the very first one is 1x I think or near that. This combined with the lights, shading, etc. make it go slower. And I just found that I’m using the Julia mode and the cutting in this one. Also it seems that the more colours an image have, the more complicated it gets to be rendered. Images that are too colourful like the “Beatle Sugar Cube” below seem to be slower because of the different colours. But sometimes the images need to be that vivid. OK if you like a plain pink shade all over your image, I don’t.

I will try to make some more tests and for example disable the cutting when/if it won’t make a difference in certain keyframes. I think that it works for me more like a guideline if I want to find a Mandelbrot shape inside that mess, for example, or to reveal certain areas of “solid” fractals to see if they have something interesting inside. I’m not sure if I can really reach these internal areas just by zooming in without cutting them first, probably I can’t.

I have read that the common timeframe people spend rendering these animations are “weeks”, so I guess I’m just starting… if I want to add a soundtrack for example, it wouldn’t work if the animation is too short. At 24 frames per second, 2 of these keyframes with the settings I’m using for this new test (25 frames inbetween keyframes) will give me a 2 seconds animation. Do the math.

Related Images:

Tags: , , , , , , , , , , , , , , , , , , ,

Mundo Fractal is Stephen Fry proof thanks to caching by WP Super Cache