Hi Everyone, in today’s entry, fractal images take the stage. To oversimplify, fractals are the patterns formed by solution sets of certain types of equations. The solution sets have distinct properties, such as self-similarity and infinite detail; no matter how you may magnify or shrink the values you will find stucture that looks similar to every other scale, and there is always more detail to be had. The equations’ parameters alter as one or more variables are incremented in some fashion as thousands, millions, or greater multiples of solution coordinates are generated.
A coloring variation of a Julia fractal
(Using Fractint)
When I started exploring fractals, making an image was a process where similarities to photography were more obvious. I bought a little program that was advertised in the back of a science magazine. It came on a single floppy disk and used the state of the art EGA monitor we had. The IBM AT’s massive 2 (two) *grin* megabytes of RAM was plenty of memory. The images that resulted were 16-color banded snapshots. You’d alter the parameters of an equation, assign your 16-color palette using a coloring algorithm and save the file. It was a lot of fun, but soon business took precedence, and I had no time to mess with it in any concentrated way. In a couple of years, the AT had died and we had no computer access for a number of years. The next time we did, it was *capable of going online* and I found the Fractint and fractal-art mailing lists. *Big Smile, happy me*.
The freeware granddaddy of fractal generation programs, Fractint was (still is) capable of generating all fractal types, but the most advanced version is still a DOS program. Fractint boosted the color palette to 256 colors, allowing the construction of nice gradients which, in turn, can be designed to mimic lighting, resulting in images with apparent depth and form. The image could be skewed, rotated, zoomed in or out, etc. This brought the creative process even closer, in my mind, to photography or, even, painting. Even the types of pictures were familiar, with a little help from imagination…
The Portrait:
The Grinch’s Evil Fractal twin. (Using Makin Magic Fractals)
The Flower Shot:
A subdued Christmas flower made, frame and all, in Ultra Fractal.
The Pattern Shot:
Pattern from fractals, note the self-similarity: the forms are not identical.
(Using Fractint)
The Wildlife Shot:
A spiral of fractal bats; look closely at the ears. (Using Fractint)
The Abstract:
This image was made in Atriatix, and is controlled while the program is generating the image; the image is made up of trajectories.
Lastly for today, the Landscape:
Fractal fog moving onshore *grin* (Using Dave Makin’s Makin Magic Fractal program)
For several years I worked along trying to develop my own fractal art. I hope to be getting back to work and catch up a bit after a 5-year interruption in that path. I’ll be trying to learn the new version of Ultrafractal. I had only used my old version for a few images, mostly using a flow-dynamics formula rather than a fractal equation. The program is a sophisticated image manipulation program and some of my favorite fractal artists are bringing out truly painterly pieces-some using more than a hundred layers; some experimenting types have even written their own little ray-tracers to work in it. I’m a bit worried about getting back on the bronco!
To learn more about fractals from a math perspective and find out the practical side of fractals click on this page by Omegaman_UK.
For a short, interesting overview of the Mandelbrot Set, see this piece, here. Disclaimer: this page is on a commercial software site and my linking to its informational material is not an endorsement of the product, with which I have zero familiarity.
Thanks for comin’ by, have a grand evening!
Cheers,
pete
Just beautiful! -k-
Hi Karol, Thank you! I appreciate the feedback, especially in the last weeks, when I suspect you folks in the advanced course are hopping.
Cheers!
pete
That is what I so love about fractals! The things they can turn into like bats and grinches. Well actually I love everything about them, the shapes, the colors, the flow, the iterations. They are so fascinating.
Anita
Hi, Yay! I’m glad the fractal images work okay. I was hoping they’d be too much a departure from photos, though to me they are me working out photos to take with the tools provided in the math, the same sort of mental workflow about point of view, center of interest, framing, contrast, lighting(to the extent that can be done in whichever software I’m using) and even simulating darkroom moves by building the palette to have highlighting and cycling the colors to see how best to give it apparent form. At least I hope folks are okay with them, the oricinal idea for this blog included using ‘em. I wonder how many variously-realized and colored spirals folks can stand before they apply to WordPress to ban my blog, lol.
I’m realizing that I still like the coloring in Fractint better than I do the soft pastels and earthy tones that are available in Ultra Fractal, although Ultrafractal is a hugely powerful image manipulation program compared to Fractint. Some purists, who only want to show what the math is doing, eschew UF but the artistic possibilities in UF are enormous, if you really learn all its intricacies. Geez, i’m scaring myself out of trying to relearn it, heh.
The physics side of fractals is becoming spooky. Finding out that magnetic fields have Mandelbrots in the outer edges; that none of the “strings” in all of those twists, sprirals and branches overlap. My imagination circuit breaker overloads at that point: “Welcome to Strange Attractor #879.99087, Home of today’s deja vu” *grin* Self-similarity made awareness.
Thanks for coming to look ‘em over and for letting me know your response!
Cheers,
pete
I know! that mathematics of it is awe inspiring to me! I think these fit in here just fine, it doesn’t have to be an all or nothing blog. They add another area of interest. The first fractal program I got was Mind Boggling fractals, which I probably still have here somewhere but if it’s on a floppy I’m out of luck
Ah, Paul Carlson’s proggie! Back when I first got online and stumbled onto the FractalArt mail list, I used to hoard the Carlson formulae; they were high-percentage wonderful metallic object generators for me. Cool stuff!
And thanks, your comment reminds me that it would be a good idea if I transferred everything on diskettes to the next storage unit going extinct…CD. really ought to get a dvd burner some day.
Cheers!
pete
I find fractal art fascinating. I have a friend who works with them quite a lot, takes them into Painter to complete her abstracts. She has just finished an online class in “fractaling” — my made-up word
and has posted them all in her blog, The Accidental Artist. You can find her work here; you might enjoy sharing your’s with her in a comment there. http://anaccidentalartist.blogspot.com/
Happy designing!
Hi Barb, thank you for recommending your friend’s blog; I love seeing what folks are doing with fractals currently. I love the bold colors and graphics available in Fractint, but the tools available to reach a higher vision in Ultra Fractal are powerful. Some of the work being done currently looks downright visionary. Probably, someone Out There, depending on which books one reads, is showing us with fractal-based art what the next level of understanding of the world is that physicists will work out later. Mindboggling, if true. Everyone’s about five years beyond me into the use of Ultra Fractal. That’s my next learning curve to climb; relearning Ultra Fractal and finding out how to use the new bits! Intimidating, to me, at least. I’ll certainly be spending some time at your friend’s site, as she might have just finished the course for which I’ve signed up *smile*.
I apologize for the lack of a coffee urn for your visit, I’m only allowed herbal tea by my doctors, the Philistines. Thank you for taking the time to read my post and leave your thoughtful note!
Cheers,
pete
Hello Pete!
All of your fractal images are wonderful job!
I think it will takes me about million years to be the expert photographer like you.
The photo of “A coloring variation of a Julia fractal” is very nice one.
I like the way you set the dark background, and the most interesting is the contrast colors of the object.
I try to take pictures of my four legs friends by close up their faces, however, all of them came out so terrible especially their eyes color, sometimes it came out red eyes, or glowed in the darkness.
I would like to ask your advice, please.
Thank you.
(P.S. Thanks for visited Joa Ying’s blog, and support her howling.)
Hi Rainbow, thank you very much for your kind comments on the fractal art, I’m glad you liked it! The Julia fractal always sort of reminds me of some Royal person’s jewelry, although in other images I started to color Julia fractals in odd ways, on purpose, because .there are only so many times you can make metallic swirls, even if they are flowing into great shapes, lol.
As far as photography goes, I don’t consider myself an expert, just an old hand at it. I make lots of errors as I go and adjust…and, of course there are always many more pictures that I’m not happy with than those that I like, or will display. Besides, I just *AM* a million years old, or at least it feels that way *grin*.
I’m sorry, but I’m so late getting to these I will have to wait until tomorrow to write down a couple of things about taking pictures of your fuzzy friends. More tomorrow…
Cheers!
pete
Wow, these are amazing!! So beautiful – and they do have a photography feel to them. I think it’s great to show other interests, too. I especially love the landscape one with the blues and silvers. It has wonderful color, shapes, and textures. It looks like a fantasy world. I think the idea of art based on math is so fascinating. (Have you played with tessalations, too? Tessella is a fun plug-in for Illustrator and Tesselmania is an older kid’s software program that I love playing with. There is now a free download for it – but you can’t save in it.)
Hi Ellen, thank you for the “head’s-up” about Tesselmania, I went and peeked and it looks like my kinda toy. The M.C. Eschers of the future are being well-served there, lol. I haven’t done much with tesselation, save to color forms using units made from whole and angularly cropped graph paper spaces. In the early 90s I started playing with a program called, “Arabesk,” that could be used with POV-Ray to make remarkable mosaic walls or floors, but I never got to use it that way, myself, before time for graphics got scarce. I don’t see the program around anymore; a pity.
I’m so glad you enjoy the fractal images-and thanks for commenting on the photographic ‘feel’ of them. Currently, the most-used program makes much more painterly images, at least in my opinion. I’m looking forward to working with that as well…I’m a frustrated oil painter. *smile* The landscape fractal is from a software by Dave Makin, now a wonderful artist and formula writer using Ultra Fractal. His Makin Magic Fractals was an eye-opener for me in the time before Ultra Fractal, incorporating virtual lighting and shifting the twisting roots into a 3D look like nothing else I’d seen. I hope that formula made it into his Ultra Fractal formulae.
Thank you so much for reading my post and taking the time to leave a note to let me know about the tesselation proggie and to leave such nice supportive comments!
Cheers!
pete
Hi Peta,
Thanks for using my software !!
I hope you take the plunge into Ultra Fractal 5 – it’s amazing what it can do now
bye
Dave
Hi Dave,
It was entirely my pleasure! I had a ball with your program, thank you for making it available for use!
I have begun doing what my computer allows with UF 5 (currently in Janet’s second class). The computer I use faints a lot when it finds fractal math to do…overheating and shutting down but, as you say, the UF tools are just *amazing* now. I’m looking forward to finding a comp that will handle it better, as I’m re-discovering the addictive nature of working with fractals.
Thanks again, Dave!
pete