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What is a fractal?
Here are some definitions
1) A shape that can be repeatedly subdivided into parts, each of which is a smaller copy of the whole. Fractals are generally self-similar and independent of scale.
2) A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way. Some of the best examples can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and they may actually have a self-similar structure that occurs at different levels of magnification.
3) A term coined by Benoit Mandelbrot in 1975 to refer to items with fractional dimensions as opposed to the integer dimensions such as 1, 2 and 3 associated with length, area and volume. Often used to refer to a structure bearing statistically similar details over a wide range of scales. Fractals describe shapes that are "self-similar" -- that is, shapes that look the same at different magnifications. To create a fractal, you start with a simple shape and duplicate it successively according to a set of fixed rules. Oddly enough, such a simple formula for creating shapes can produce very complex structures, some of which have a striking resemblance to objects that appear in the real world.
4) Fractals share holographic properties.
5) A geometric shape or pattern that is self-similar and has fractional dimensions. Natural phenomena such as the formation of snowflakes, clouds, mountain ranges, and landscapes involve patterns. Their pictorial representations are fractals and are usually generated by computers. They are repeated at every scale and so cannot be represented by classical geometry. Fractals have statistical self-similarity at all resolutions and is generated by an infinitely recursive process. An algorithm, or shape, characterized by self-similarity and produced by recursive sub-division; more generally the branch of mathematics named and explored by Benoit Mandelbrot.
6) Fractals are like clouds. When looking at the same cloud some will see flowers, while others may see bunnies, or viking warlords frolicking in the snow. Each person sees something different. What do you see?
Examples of fractal properties
From Quantum Theory Made Easy – part one:
Quantum physics
"....shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated 'basic building blocks', but rather appears as a complicated web of relations between the various parts of the whole. These relations always include the observer in an essential way."
Chaos theory
“The fractal geometry of chaos theory offers a curious picture of wholeness, rather than sheer disorder or perfectly crafted design -- something between symmetry and anarchy: broken symmetry. These fractals are like the fragments of a shattered hologram. If a hologram should be broken into pieces, an approximation of the whole picture could still be seen in each of its many shards. Woolley suggests that the universe is like the many fragments of a shattered hologram, and scientists can discover secrets of the whole "enfolded" universe by examining these fractured crystals that are "unfolded" and consequently accessible to our investigation. Holography, like fractal geometry, is of great practical value in the compressing and decompressing of digital data and images.
Let's take a moment to regroup. There should be some sense of non-local connection emerging here entangling Dali's illusions, fractals, spirals, holograms, compaction's dimensions, encoding, symmetry, asymmetry, broken symmetry, stereograms, and all those ideas yet to materialize. Chaos puts our fragmented world back together as a crystal of broken symmetries with many facets -- as fractals . We must come to appreciate the mystery of the diamond mind, which attains its true beauty only when it is broken by the hand of an artist. These swirling images of the whole raise us to dizzying heights, but the wholeness we experience is not the limitless expanse of the universe, but a passageway through creation in which we also have a hand to play.
From Fractals In Nature:
Most mathematics that we study in school is old knowledge. Around 300 B.C. a mathematician by the name of Euclid organized the geometry we have been studying this year in class. You can thank him for all the beautiful postulate and theorems that we now have in our math toolboxes. Much of fractal geometry, however, is new knowledge. Fractal geometry and chaos theory are providing us with a new way to describe the world. Many objects in nature aren't formed of Euclid’s squares or triangles, but of more complicated geometric figures. Many natural objects - ferns, clouds, seashells - are shaped like fractals. Fractal geometry is a new language used to describe, model and analyze complex forms found in nature. Chaos science uses this new fractal geometry.
How it all works
The basic technique of these fractals can actually be explained without resorting to confusing mathematical equations and jargon. It's rather simple, really.
First, give every point on the screen a unique number. Now take that number and stick it into a formula; you'll get a result from the formula. Take that result and stick it back into the formula. Keep doing this and watch what happens to the numbers you get. Color each point based on what happens.
That's it. Really—that's it. Now, with most formulas it probably won't do much of interest, but with the formulas used in fractal creation, some interesting things happen. Sometimes the numbers you get by feeding the results of a formula back into the formula (iterating) explode into enormous numbers, that just keep getting bigger and bigger. Those points get colored one way. Other times, the numbers "home in" on a number, getting closer and closer to it. They get colored a different way.
The interesting thing—and the reason fractals work at all—is that sometimes, just a tiny little change in the number you start with can completely change what happens as you keep iterating the number. And the boundary between numbers that explode and numbers that home in is complicated and twisted—it's the shape of the fractal.
The enormous task at hand
Calculating fractals this way involves a lot of work. A small fractal image—perhaps only 640x480—contains over 300,000 points. Each of those points may require running a number through the fractal formula more than 1,000 times. This means the formula has to be computed more than three hundred million times. And that's a mild example. Extreme images (such as poster-size fractals) can involve more than one trillion calculations. Fortunately for the impatient among us, modern computers are fast enough to do the job in a few minutes. Large fractals might take hours or days, but exploring fractals has never been easier.
Not quite so similar
Many fractal types get wildly different as you zoom in. They're still self-similar, but they're not rigidly self-similar. This is what makes fractal exploration so intriguing. The features you see as you zoom are always changing—teasing you with a little bit of familiarity, and tantalizing you with new and unexpected twists. With just a single fractal shape, you can explore forever and never see everything it has to offer. The further you zoom, the more likely you are seeing something that nobody has ever seen before. And with modern computers, it's very easy to zoom and zoom and zoom. With just a few clicks you can have zoomed so far that the original fractal image is larger than the sun.
My Biography
For years people have been asking how I got started with fractals. Here is my response:
I began exploring fractals back in the early 1990s when a friend introduced them to me on his 386 computer. We would wait hours for a single 640x480 picture to render itself. It wasn't until 1994 that I was able to explore them using my own PC. I'd purchased a top of the line 486 class machine and spent the next six years creating fractal art. My friends and family suggested I sell my fractals as T-shirts and counted cross stitch patterns. After a couple years of research I started my T-shirt business. I prided myself on making high quality one-of-a-kind fractal T-shirts. Many of the ideas I have implemented through my web site have been copied by others. For years I was the first to make unique fractal T-shirts, fractals as counted cross stitch patterns, fractals as affordable two-hour videos, fractals for PC-Jigsaw Puzzles, etc. When I filed my first copyrighted works collection I had created 13,000 unique fractals! But the real explosion didn't happen until I upgraded to two faster PCs in 2000. Since 2000 I've averaged 10,000 new fractals per year. In 2006 I made 30,000 new fractals.
By early 2006 I gained a spot at Fayette County's only art gallery. My fractal art remained on display until the gallery had to shutter its doors a couple of years later. I was asked by the gallery owner, Miss Kathaleen Brewer, to run a fractal presentation for her customers. In April of that year I nervously stood before a packed room in her yellow bungalow / gallery just off the square in Fayetteville. If you go to the Art Show page you can read about how things worked out and see photos that were taken that evening. In addition to getting my start at the Fayette Art Gallery I had a three month stay at Fine Line Gallery near Atlanta. On January 9th 2007 I started this web-based catalog.
By the middle of 2007 I got a chance to run my fractal slide show animations for Sci-Fi Summer Con. This was to fill the spot for background visuals that were akin to "The Dating Game" and "trippy, hippy" in style. There was a seventies theme for that year's costume contest. At the 2007 Dragon Con I played a 9.5 hour fractal DVD for the drum circle crowd two consecutive nights. This opportunity arose from a simple request to use the overhead digital projector with the convention's DVD player. I got into the rhythms of the drums. I work with patterns daily when exploring fractals. I also pick up on other types of patterns. Some are visual, emotional, while others may be audible. This crowd had 'em all. It was very cool how the drummers worked together with no clear leadership. Any one of them could dictate a new or subtle direction in their music. Their vibe fed off the audience and dancers and vice versa.
Either prior to or just after Dragon Con 2007 I was asked to perform my fractals for Strobelight's Alan Siler. His cover band was performing a set of B-52s music at Gaylaxicon 2007 and had requested that I create a particular type of "trippy" fractal backgrounds. I scoured through my entire database of fractals to find what he was looking for. Not long after that initial request I had found 12,039 matches. My slide show animation for Strobelight went well. I created numerous variations lasting thirty to fourty-four minutes in length. I was to also play a set of fractals for the dance that followed their live performance. The only criteria was that the two styles be completely different. However, there was a hitch. About thirty minutes into the dance the DJ suddenly halted the show, packed up his gear, and left to play at another gig. In addition to having the opportunity to entertain with my fractal light shows I also had sales in their art show and favorable mention from their host of the silent auction. I now use those same Trippy themed fractals, plasma clouds, and fractal clouds for my Trippy Jigsaw Puzzles, Trippy DVDs, and other Trippy themed uses.
By early 2008 I was asked to create an opening bit for the Roswell CABY awards. I was assigned to work with musician Darren Nelsen. Ultimately what came of that was my venture into high definition fractal animation and exploration. At the end of the CABYs Lisa, a math teacher, approached me with an invitation to present my fractals to her students at Roswell High School. She wanted me to show the same animations and to talk about my experiences making them. I invited Darren to participate so he could tell the kids how he had used fractals to make his score from the awards ceremony. That gave the two of us an opportunity to entertain and educate 800 math, arts, and music students from the fourth to twelfth grades. At around that time I played the same HD fractal animations during the Horizons High School reunion. I was a student at their Ponce De Leon school back in the 1980s.
By the middle of 2008 I had another show to run. This time I was asked to create the fractal equivalent of Carl Sagan's "Cosmos". This was for the 20th year anniversary party of The USS Republic, a Star Trek fan-based organization. I worked for three months to create a sixty minute animation. Their 20th anniversary party was held during Sci-Fi Summer Con. So in a way this was my second time playing my fractal light show at that convention. By October of that year I got an email from Georgia Tech asking me to create an art show for their Ferst Center of the Arts. I was granted complete artistic control of what I wanted to do. They also wanted me to perform for the fourth graders at Centennial Place Elementary. As the end of my month long stay was coming to a close I was asked to stay an additional month. It was during that month that I ran my fractal animations for two groups of students from Centennial Place. I also gave them a tour of my hanging art and split each group into two parties. While one party worked at solving a hand-made fractal puzzle the other party created their own fractals. At the end of the day I gave the fractal puzzle to the students via one of their teachers.
By December of 2008 I began my collaborations with musician Michael Thomas Roe. The two of us performed at Kavarna for a one hour set. The audience was captivated by my fractals and Michael's music. Although we did not specifically create for each other's talents the performance looked as if this was a carefully crafted effort. In March of 2009 I re-joined Michael on the stage at Kavarna. This time it was a black and white themed fractal presentation. Instead of running my HD fractal explorations I chose to make a two hour DVD slide show (with 44 cool transitions). At the end of Michael's set Serson, the next performer, asked me to "light me up". So I ran my HD animations from the December show. From that I had a few DVD sales right after his show. I continue to seek out new and more venues in which to perform, display, and sell my fractals as animations, DVDs, games/puzzles, printed art, video art, etc.
Other Accomplishments:
I have been a foster father for DeKalb County for 2.5 years. I was a care provider for handicapped infants at Changes. I went to DeKalb College to learn Radio/TV broadcasting. After that I went to DeKalb Technical for two years learning to be a pressman (just for the fun of it). In 1990 I began advocating for the civil and human rights of Georgia's Mentally Retarded (MR). In 2006 I came back to the Atlanta area for two reasons. One was to help my mother and handicapped brother. The other reason was to seek gallery representation and sales for my fractals. Since my return to the Atlanta area I have had numerous opportunities to sell, display, and perform my fractal works. I find myself shifting more and more into running fractal presentations for students, running my DVD and HD video art for musicians, DJs, and VJs. My goal is to eventually secure my own gallery space.
(Questions & Answers)
Q: What happened to your web catalog?
A: I streamlined everything
Q: Do you still sell things in person and at art fairs?
A: Of course.
Q: Will I still be able to buy directly from you?
A: Sure thing.
Q: Do you take online payments?
A: Cafe Press handles that.
Q: How do I make an order through cafe press if what I want is not there?
A: The easy solution is to follow these steps:
1) Choose the fractal(s) from my web site that you wish to buy
2) Choose the product type(s) you would like from my Cafe Press account
3) Send an email to me indicating your fractal choice and the Cafe Press product type(s) you wish to buy
4) I will make the upload(s) necessary and send a confirmation link to you when the item(s) are ready for purchase
5) Please review your product before you pay. What you see is what you will receive.
Q: How can I use your video art with my HD TV?
A: That depends on the sort of video inputs you have on your set and the type of video art you wish to play.
1) DVDs are self-explanatory. You'll get the best results if you use a DVD player with HDMI upconverting. Simply attach one end of the HDMI cable to your HDMI-enabled DVD player and the other end of the HDMI cable into an empty HDMI input on your HD TV. That one cable will carry both your audio and video signal.
2) If your DVD player does not have HDMI or if all your HDMI inputs are in use here is the second best way to get video into your HD TV. Use component cables to attach your DVD player to your SD or HD TV. Simply match the colored jacks to the colored tips of your cables and you're golden. It really is pretty easy to figure out.
3) Does your HD TV have PC input as a VGA port? You will need a 15-pin VGA video cable to run between the video card or VGA port on your PC to the VGA input on the rear of your HD TV (or digital projector). Just be sure that it supports all the resolutions that are on your recording. Many of my fractals are saved at 1024 x 768 DPI. Most HD TVs with PC input support this video resolution or higher.
Q: Will you change the colors of your fractals for me?
A: I do not change the colors of my fractals for customers.
Q: I saw this really cool fractal somewhere. Can you make it for me?
A: I do not do that sort of thing. I suggest you buy the art from that individual.
Q: Can I use your fractals for visual stimulation of my handicapped child?
A: Absolutely. My fractals are an ideal way to aid anyone with physical and cognitive difficulties.
Q: Are your galleries for sale?
A: No. You may browse my InterNet galleries to make your selection(s).
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