 |
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. On January 9th 2007 I started this web-based catalog.
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). From March of 2002 through September 2003 I was the sole care provider for my older MR brother. I stepped in to help him after a horrifying experience at his last service "provider" where he was abused physically and psychologically. While in my care I trained him for a freer life at Annandale Village. After caring for his needs I bought a home in Peachtree City. In 2006 I came back to the greater metropolitan area for two reasons. One was to help my mother and handicapped brother. The other was to seek gallery representation and sales for my fractals.
(Questions & Answers)
Anti-theft / Anti-piracy
Q: How do you protect your art from being stolen / pirated?
A: For each printed fractal I have my copyright notice along the bottom edge. Obviously that is not a deterant to theft. I may start using "secure" papers if it becomes a problem. For video tapes I use an unique linear format.
Q: What the heck is that?
A: Here's how it works: First I dumb down the fractals to 800 by 600 so it can be seen on a regular TV set. Then I record from my PC to a S-VHS / VHS recorder. PC Video Art always has a random arrangement of the same set of fractals. What I am doing is capturing a unique linear version each time I make a video tape. This means no two original tape recordings are alike. So lets say someone buys from volume ten. When a bootleg is made the illegal duplicate will have the same sequence of fractals as the original does.
Q: What if a bootlegger makes a copy from tape to tape?
A: No biggie. The VHS format is prone to loss of quality each time a copy of a copy is made.
Q: Okay. So how does that stop people from stealing from you?
A: It doesn't stop the action. Basically if it can be seen or heard there is a way to steal it. What I do is try to deter the casual thief / pirate.
Q: What other deterants do you employ?
A: I will not disclose all of the options available to me. One thing that I do is encode the customer's name or other information into my Video Art Any unauthorized copies will carry the customer's name and/or address. It is unlikely a pirate would want that revealed the world at large.
Availability
Q: I absolutely LOVE these cool fractals you've made. How do I know if it is sold out or not?
A: Use the Prints Sold page to see if you can still buy the one(s) you want. You can find the Prints Sold page from the Prints page. To access all site links from one location simply click on the HOME page link at the top of every page.
Q: What about your cross stitch patterns? How do I know if they are sold out?
A: Use the Prints Sold page.
Q: Will you ever make one-of-a-kind fractal T-shirts again?
A: Not at this time.
Customer Service / Privacy
Q: Do you maintain a buyer's list?
A: No.
Q: If I order something from you will you sell or disclose my personal data with others?
A1: No.
A2: If you've bought a software title or cross stitch pattern your name and address may be included within those items. Technically I have not revealed your information to others.
Fractal Catalog, Galleries, Kiosk
Q: You can't possibly have that many fractals. How do I know you aren't lying?
A: Until you can see my On-Line catalogs you don't.
Q: Have you thought of naming your fractals?
A: I am undertaking the process of giving cool titles to my Limited Edition prints.
Q: Cool beans! When can I see them?
A: Click on The Name Game to see 466 titles. The arrangement of The Name Game page will change as I add new fractals.
Q: Would you be willing to set-up one of your fractal art kiosks for my gallery or business?
A: Sure. We'd have to discuss what you have in mind first.
Q: What sort of kiosk options do you provide?
A: Rentals, Oddball cases, artsy cases, various vertical and horizontal mounts for one or more users.
Q: Would it be cool if we built our own kiosk cabinet around your computer stuff?
A: Certainly. As long as your enclosure doesn't look ugly, isn't racially or sexually offensive, won't lead to a fire, and provides ample ventilation I'm cool with it.
Q: What sorts of stipulations do you have?
A: Please visit Fractal Kiosk for examples
Q: If your art is limited to 20 prints how will I know if the fractal I want is sold out or not?
A: This question has already been addressed. Look for the Availability heading for the answer.
Funny Guy
Q: Some of your other work is pretty damn funny. How do you come up with those things?
A: Often it is the first thing that pops into my noggin. I'm a smartass. What can I say?
Q: Who really comes up with these questions?
A: Someone who really wants to know.
Q: I saw you braggin' about being a super genius on your "allfractup" Myspace account. Is that true?
A: Absolutely. I was bragging about it. I was smart enough not to pay the forty bucks to take a test from Mensa wasn't I? Case closed :)
Q: What is it like to be a super genius?
A: No different than being an intellectual god. The only downside is my dyslexia masks my true potential.
Integrity / Making Fractals
Q: Are the numbers on your home page the most current?
A: No. I normally have additional fractals in reserve. Or I begin making new ones immediately after posting updated figures.
Q: Why do you keep fractals in reserve when you are reporting how many you have?
A: There are times when the few new ones that I have don't justify a modification to my web site. I mean think about it...updating the page each time I make one new fractal? That is folly in my mind. So I wait until I feel like making additions or updates to the site. Plus it takes time to run a thorough duplicates scan of all my work.
Q: Do you compete with the sales of your vendors?
A: Not if they have an exclusive contract. Any contracted art my vendors sell can only be purchased through their services and/or location. If you like a piece that is 40 miles away (one-way) it is unlikely you would drive to a vendor's location to make a single purchase. Therefore I do offer sales of the same pieces you find on the Orders page (unless they are contracted for exclusive sales. A notation is added to any locations that have such a stipulation.)
Q: Do your vendors sell the same items?
A: I try to prevent cross sales of the same art works within a specific geographic area. That allows them to have a unique selection that someone else a few miles away does not have. If a vendor does not care about competing markets selling the same items then I feel their wishes should be honored. I try to be fair.
Q: Why are some of your vendor prices higher than yours?
A: If they have purchased the item outright they have the legal right to sell it for what they like. If they are on consignment the prices should be cloes to the prices shown on this site. I set the price for all art sold through consignment. Each vendor may want a different cut of the action. I no longer reduce my take just so the final cost is in line with what is sold here.
Q: Why not use materials from outside the USA? They make things as good as ours and it is cheaper.
A: I've heard this arguement before. To that I say this: If they are just as good as what we produce then Americans should buy American made goods. Supporting our own countrymen keeps this economy healthy.
Q: How long does it take you to make your fractals?
A: Trade secret. There is no set rule to how long it may take to create a new fractal. Factors that determine these things include resolution, level of detail, number of deep zooms performed, the type of rendering I have chosen, etc. I have spent 50 hours to render a single fractal. On others I could spend DAYS.
Q: Is it worth it?
A: I assume you mean is it worth it to create cool fractals. Absolutely.
Q: Yeah but your sales so far have been really low. So why keep makin' 'em?
A: It takes time to create momentum. A reputation for quality doesn't just pop out of the air over night ya know. I spent over a year at DeKalb Technical (adjacent to DeKalb College Central Campus) learning how to become a pressman. That was done out of fascination with learning something new. It was from that experience that I realized how fun it is to print. I was already making fractals at that time (mid to late '90s) so it was easy to apply that knowledge to my art. 'Sides I love making fractals.
Q: So if I really want a fractal that is out of print you won't make an exception for me? What if money is no object? Ya know, everyone's got their price.
A: There is no point in having Limited Edition prints if I break my own rules.
Q: Yeah but they're just rules. What is your price?
A: Hmm...Can you afford to buy back ALL of Native American Indian soil, hand ownership of it back to all of the American Indians, restore it to its original splendor, then re-create a nation that is not dependent on foreign fuel sources? Yeah...I didn't think so.
Payment / Where to buy
Q: When will I be able to buy directly from your web site?
A: You can do that right now. In the form of cash (for in person transactions), checks and money orders. I will not be offering InterNet based electronic sales. If my vendors choose to do so that is their business.
Q: Which vendors sell for you?
A: Please refer to the Orders page for vendor contact information.
Q: How about those automated machines that you see selling or renting DVDs?
A: Its like you're reading my mind. Stay away from the curtained off area if you are...I have looked into using those machines. They are pretty pricey. Locating the right venue is the tough part.
Q: Do you accept PayPal?
A: No. PayPal is not secure.
Q: Can I wire the money to you?
A: No.
Q: What forms of payment do you accept?
A: Cash, Checks, and Money Orders. All monies shall be in US currency only. Checks and money orders must clear my bank BEFORE any works are produced or shipped. Persons paying by check or money order will be the ones I send the product(s) to. I am considering a C.O.D. (cash on delivery) option for items that are not customized or personalized.
B: My bank has an On-Line service where I can scan your check and get near instantaneous validation. They call it Online Depositing. With this wonderful tool I am able to expedite the turn around process. The turn around process is how long it takes to get the product you ordered out the door and in your hands.
Q: I live outside of Georgia and/or the United States. How do I make a purchase?
A: Please review the answers already provided.
B: My vendors may accept credit card payments. Please refer to the Orders page for their contact information. In which case it may be possible to place an order over the phone and have the item(s) shipped to your location.
Q: Do you accept orders over the phone?
A: Sure. But payment must be in the manner prescribed on this site. A refresher of that policy is personal checks made out to me (by name), in US dollars and cents, for the exact amount of the purchase and shipping and insurance (if any.)
Q: I've tried calling but all I ever get is a busy tone or an answering machine. What gives?
A: If you've gotten the answering machine please leave a clearly spoken message with your name and phone number. All messages are answered. If you have gotten a busy signal please try again later. I make my uploads from a dial-up connection. If you feel you cannot get through by phone you can always reach me via E-mail.
Site Related
Q: I've made searches on Google or other InterNet searchs and I have to tell ya yours isn't coming up first. You said you were the first to create a lot of these product types. Wouldn't you be ranked as first?
A: Each search engine may have their own way of ranking the popularity of sites. I basically use Google for all my searches these days. Until recently they were still linking to some of my oldest pages or online advertisements. For instance I haven't made one-of-a-kind fractal T-shirts for many years. I've sent an update request to Google for this web site. It will take time for their "bot" to spider my site.
A02: Lots of sites have cropped up over the years to release copycats of what I was the first to offer. Some sell their knock-offs for less. Their quality may not be on par with my products. Some sites are paying for better search results. So while their sites may seem more popular than mine there is a reason for it.
Q: Why is this page so much longer than the text warrants?
A: I wanted to give myself some breathing room. I like to update things without having to fuss with page parameters each time. On many of my pages I try to keep things in check. By that I mean I keep the length of the page at the right length without being too long.
Q: Your page is slightly wider than 1024 pixels. It is such a drag having to tap the arrow keys to read what was cut off.
A: Problem solved. I set the horizontal cut off to less than 1000 pixels on most pages.
Q: Hey where'd the cool graphics from your home page go?
A: I'd heard from visitors that it was tough to find what they were looking for. This is a boon for dial-up users who can see updates to the home page without needing to re-load the graphical links each time. For Pocket PC and Smart Phone users their little screens can get right to the meat of things faster. The graphics are still on my web site. I'm just not including them in my HTML.
Q: Will you ever have all of your fractals online?
A: Not likely. By the time I finish uploading 80,000 fractals I may have 100,000. Then there is the matter of my batch processors. Sometimes these programs reject fractals for reasons I have yet to determine. So while I have a great many fractals only the majority shall ever be visible in the catalogs. I use the batch processor software to create the catalog pages, to re-name & re-number the fractals in sequential order, apply copyright notice, and affix the "SAMPLE" graphic to all of the fractals.
Q: Will you ever run out of web space?
A: There is that possibility. Currently I have 97 GBs of capacity. That should be enough to grow into over many years. Assuming of course that I do not make too many program or screen saver additions to my site.
Q: Why aren't you numbering these Q&As?
A: It is easier to make changes if they aren't numbered. That way I don't have to spend half a day re-numbering things any time I insert or delete something. I added color to the "q" part to give readers a visual cue. As you can see I've attemtpted to organize the questions.
Q: I picked up one of your free CD-ROM catalogs. Do you mind if I share it with other people?
A: You can give the disc to whom ever you like. The information on those is no longer valid. Prices were updated in January 2007. Since they were made I have changed product types, features, and lots of other things. Still you are free to share it with others.
Q: Can I make a copy of your CD-ROM catalog?
A: You can make an exact duplicate of the disc. So long as you do not alter the contents of the disc or try to assert ownership of its contents you can pretty much do as you please.
Q: If there is something on your CD-ROM catalog that contradicts what I see here which source is correct?
A: The contents of my CD-ROM catalogs are all out dated. They were made prior to the creation of this web site. Assuming my site has not been taken over or altered without my consent? This site is the most current version.
Technical / How-To
Q: What sort of hardware do you suggest I use?
A: I buy almost all of my hardware from Ginstar. They provide excellent service at prices far less than what you'll find at other computer retail stores. Their technicians are superior to the in-house techs found at Best Buy (where I once worked) pr any other PC service agency. The hardware you choose is entirely up to you. However all of my software is created on Windows computers.
Q: Why don't you make software for Apple or Unix / Linux users?
A: Apple computers cost too much. I've grown accustomed to the environment of Windows. I've tried using Knoppix from my CD-ROM drive. It was too "techie" for me. I've got a copy of Corel's user friendly Linux that I never got up the nerve to install.
Q: Well you know Apple has migrated over to IBM computers right?
A: Yes. If the price ever comes down or if the Apple GUI is sold for installation to any IBM class PC I might give it a try.
Q: When can I buy art cases for my PC?
A: I am working on assembling that page. When complete I will post an update to the Announcements page and to the Videos page.
Q: Will you have your own line of designer art computers?
A: I've thought about it. I have not made up my mind on the best course of action.
Q: I saw this really cool fractal somewhere online. Can you make a copy of it?
A: I do not copy other people's work.
Q: I like your fractals. Are the colors I see customizable?
A: Thanks. I do not change the colors of my fractals.
B: I've found quite a lot of duplicates that have slipped past the anti-duplicates software that I use. So you may be able to find what you're looking for from General Use. I've since begun inspecting my fractals by hand in addition to using the detection software. The problem arose when I'd change color schemes and when I had forgotten what I had saved from previous sessions.
Q: How much of your art is truly art?
A: All of it.
Q: How will I know if your Video Art will work on my computer?
A: A Windows PC running 95 through Vista can run my fractal software. I believe it is possible for Linux and Apple PC users to run Windows programs through emulation. Try using the free downloads to see if that is the case.
Q: What is the slowest system you have tested your fractal software on?
A: Pentium 200 with MMX, 128 megs of RAM, standard XGA (1024 by 768) resolution monitor, running Windows ME.
Q: I have a Windows Media Center equipped PC. Can I use that to enjoy your fractal software?
A: Yes. If it is hooked up to a High Definition TV or PC monitor that handles 1024 by 768 or 1280 by 1024 then you will see them at their best. If it is a regular TV then I would have to create special versions. Detail on a plain television will not be as good as a PC monitor or HDTV. The best you can get is 800 by 600 on a regular TV set.
Q: Well how do I know if my HDTV / TV set can do all that stuff?
A: Consult your owner's manual, call the manufacturer, or check for information on their web site.
Q: Dude, all those cables give me the willies. Isn't there an easier way to use my PC with my HDTV or spare TV?
A: It really depends on the type of TV you have. The sorts of connectors your TV uses will determine how you feed audio and video to it. The easiest thing to do is look on the back of both your TV and your computer to see what they can connect to. If you are confused by the shapes and names these ports have there are a number of free resources both online and in your local library that can clear things up for you. If you still think you cannot do the job yourself why not hire someone to do it for you? Places like Best Buy and Sears have teams of certified professionals who can do the job in a snap.
|
|
