Frequently Asked Questions about FRACTALS and other subjects related to this site and its images

(Last updated April 1st, 2024 to include some links and text revisions. A small part of this text was taken from this site. It’s being rewritten as the site is being rebuilt. Some links are directed to Wikipedia articles)

Fractals, Fractal softwares and Fractal Art

Q: What is a fractal? What are some examples of fractals?

A: A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale.

There are many mathematical structures that are fractals, like the Sierpinski triangle, the Koch snowflake, the Peano curve, the Mandelbrot set, and the Lorenz attractor. Fractals also describe many real-world objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes.

According to Benoit Mandelbrot, who invented the word: “I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means “to break”, to create irregular fragments. It is therefore sensible – and how appropriate for our needs! – that, in addition to “fragmented” (as in fraction or refraction), fractus should also mean “irregular,” both meanings being preserved in fragment.” (The Fractal Geometry of Nature, page 4.)

Q: What fractal generating softwares do you use?

A: I have tried many fractal generators since I started around 1996-7 (I think?). I started with FractInt (still in DOS!) when it came in a CD in one of these computer magazines with lots of freeware/shareware softwares very common in the early 90s, then I discovered and moved to Ultra Fractal at some point in the early 2000’s, then when Apophysis appeared I also started using it a bit, and I briefly tried the Mandelbulber some time ago, but as it required too much computer processing back then (like most of the flame fractal generators) I kind of let it aside… along all the other softwares. I was getting bored with fractals after some time and quite entirely using all of these (but that’s for reasons which I might have explained in the old site and maybe I will explain here too as they never have really gone away…). Then after a long period of getting bored with fractals I discovered Jwildfire, which is a much funnier software to play with if you want to create flame fractals. After a while I decided to give the Mandelbulb a try again (but using Mandelbulb 3d instead), and it’s what I’ve been using the most lately.

Since I started, the technology has improved a lot, computers are incredibly more powerful, and a fractal image that used to take ages to be finished now can be finished or at least previewed in a very short time, making the process much less tedious. Resolutions can be higher, image qualities are now good enough for printing in larger formats… it’s much more interesting nowadays, despite the quirks. All these softwares have their own pros and cons, and it’s up to the final user to decide which one suits you better.

I might someday write about these softwares specifically, maybe as a review. I don’t have any information on using these or other fractal generating softwares mentioned here for other platforms other than Windows, sorry.

About the softwares I use

Q: What is Fractint?

A: Fractint is a very popular freeware fractal generator. There are DOS, Windows, OS/2, and Unix/X versions. The DOS version is the original version, and is the most up-to-date. There is a new Amiga version and a very good Windows version. More information here.

Q: What is UltraFractal?

A: Ultrafractal is a very powerful fractal generator for Windows. It expands the capabilities of the regular fractal softwares by allowing you to make images with millions of colours (Fractint for instance only allows 256 colours and GIF images), layering, and the option to render your images in very large sizes and also in several image formats. I think there is now a version for Macs as well.

Q: What is JWildfire?

A: JWildfire is a free and user-friendly image processing software (I guess it can be called that because it has more options than just create the fractals), mostly known for its sophisticated flame-fractal generator (more about fractal flames in the Apophysis answer below). It is Java-based, open-source and runs on any major computer platform. There is also a special Android version for mobile devices (although quite limited I must say, it just creates batches of random images and you have no control over them).

Q: What is Mandelbulb 3D?

A: Mandelbulb 3D is a free software application created for 3D fractal imaging, mostly to work with images called the “Mandelbulbs*”. Developed by Jesse and a group of Fractal Forums contributors, based on Daniel White and Paul Nylander’s Mandelbulb work, MB3D formulates dozens of nonlinear equations into an amazing range of fractal objects. The current banner on the front page of the site was created with that.

*The Mandelbulb is a three dimensional manifestation of the Mandelbrot set. It is an infinitely complex, naturally occurring fractal object.

The Mandelbulb was discovered by Daniel White and Paul Nylander, and developed collaboratively in the Fractal Forums community. These individuals set out to find a three-dimensional equivalent of the Mandelbrot set, and they found what they were looking for.

Using a spherical coordinate system, and some ingenious math, White and Nylander projected the Mandelbrot set into three dimensions, creating the Mandelbulb. In 3D-space, we see a more fully realized rendering of the Mandelbrot set. While the flat set exhibits infinite complexity, the Mandelbulb reveals that complexity in a fuller magnitude.

Q: What is Apophysis?

A: Apophysis is a fractal flame editor and renderer for Windows. It was created by Mark Townsend by translating Scott Draves‘ original C code into Delphi and adding a graphical user interface. It has since been improved and updated by Peter Sdobnov, Piotr Borys, and Ronald Hordijk (the SourceForge project developers). It is open source and licensed under the terms of the GNU General Public License (GPL).

Q: Where can I get more information about other softwares used to create fractals and information about fractal art?

A: Try this link.

About my fractal site(s)

Q: How do I find out what’s new since my last visit?

A: As it’s a blog format, entries are done chronologically. Just start browsing from the last post you read. A few posts might have minor updates, if the updates are important (like adding more images to a specific gallery), it will be reported.

Q: Is there a chronological sequence in the images, being the first images you ever did posted in the first pages, or should they be viewed following a specific order?

A: No. I have them all mixed. Of course the newest posts may include just newer images after all the old ones were posted. Some of my old images are still amongst my favourite images after all this time, so they deserve the same treatment as the new ones. The galleries – when available – will be separated by the software that was used to create the image.

Q: Do you make 50 images every day? How can you post so many images like that?

A: Not anymore. There was a time that I probably could do that, though. And this was not only frustrating, but incredibly boring and very “un-creative”. It made me almost quit making any image for a long time. But… the site needs to be updated/cleaned up/organized from time to time, sometimes there might be a bigger update than others. There will never be a scheduled method of posting though, there will never be an obligation of posting one image or a post every day.

If I post say 3 or 4 galleries with around 15 images each on the same day it’s just because the images I’m posting are already made, ready to be posted, some are even 10 years old or maybe more and probably it was because I’m updating something in the site configuration or layout. I’m in sort of an updating phase more than a creation phase, I’m just sorting things out and cleaning the dust before I’m back to making new images, although I haven’t stopped making new images.

Most of these images now aren’t fresh creations, I’d say 80% are old images about 10 years old or even more. In each gallery there will probably be some relatively newer images than others (not often though like in the Fractint galleries, where most images are about from the same era, same with the Apophysis images), but all these weren’t done all at once right before I published the post.

Q: Are your images public domain, open source, freeware (these last 2 words apply more to softwares than the images, though)?

A: No, no and no. Despite some of the fractal generators used to make my images being open source/freeware (which are two very different things, BTW), the images are all copyrighted. The images here can be saved in your computer and have no restrictions of viewing or downloading (it’s virtually impossible to prevent anyone from doing that no matter what), but please respect the copyrights and if you are going to use any image in any commercial project, please ask for permission. Most of the images on the site have a watermark (carefully placed to not mess up the image but to keep them from being misused), which should be kept at all times and won’t be removed in any circumstance. Images without a watermark may or may not be furnished for certain projects, you should ask first for approval. The images may have varying degrees of JPEG compression, I tried to keep them at a quality level that won’t affect their display on screen and make them load a bit faster to not mess up with the hosting server but these will not let you print them with the full quality they can have. For a quality print, you’ll need better rendered versions than those on the site. If the images are in PNG format, they will probably have less compression and its compression doesn’t affect the quality as much as the JPEGs. I’ll try to keep the images around 1200 pixels wide the most, except when the image needs to be presented larger or smaller than that for any reason. The other dimensions will vary accordingly, proportionally to the aspect ratio of the image.

Q: I can’t see any of your images. Why?

There is no restriction to any browser or operational systems that I know of. Maybe if your Javascript is turned off, there can be some problems, WordPress uses Java a lot. Firefox browsers have been a little nasty lately with certain Java scripts. I don’t recommend any special browser. The site was built to be displayed on a regular computer screen, so I have no idea how it will look like on a tablet or a phone. If the optimization for these devices is something easier to do, I might have different versions for each device. I still don’t know how to do it – I used to, but that was 20 years ago… but I think that WordPress and some other plugins included can make the pages available to different devices without any problems automatically.

Q: Why do the watermarks in certain images display a different URL than the current domain I’m viewing? Aren’t these your images?

A: I have hosted my images in a lot of sites and domains over the years, so older images which I could not update and render again in bigger sizes can still have the watermarks pointing to their very first URLs (http://www.baco.nu/fracts or http://www.baco.nu/fractals for example – these links are now long gone). I have rendered a lot of images again in bigger sizes than these first ones (different times, screen resolutions and aspect ratios have changed a lot since my DOS days of FractInt), so these might display correct watermarks or even not display any at all.

Q: Can I use your images on my site?

A: Well… yes and no. There are two different situations regarding the use of the images: You liked one of the images and want it to be your new wallpaper. Fine. Go ahead (I can’t control this anyway). The other situation is: You liked the image etc. and you want to make a profit out of it, like selling printed reproductions of the image as if it was your work on your t-shirt selling website. Or you want to use it in your band’s CD cover art as if it is YOUR image. Or you want to make a nice and big website about fractals using MY images, or you want to share them on your social media account. This is mostly illegal (mostly the profit part), these images aren’t in the public domain. If you don’t know what a copyright is, or worse, if you don’t care, stop reading here. Or you can be nice and do like these guys (R.I.P. Scott!), who wanted to use one of my images in their new CD artwork, and asked for permission to do that (of course, after paying a small fee 😛 ). Asking for permission doesn’t hurt. If you are, for example, an art or math teacher, I might just let you use the image in one of your classes or something – I was asked many times for permission to use some images in situations like this.

Another very frequent situation is the “hotlinking”, where you have a link in your site or post a link somewhere (like in a forum or social media site for example) to an image that is located in someone else’s server. This is a bit controversial, some people actually like to have these kind of links elsewhere (it’s free promotion anyway), but this way you’re stealing someone else’s bandwidth, which is something they have to pay for, not you. This is also wrong and it is called “bandwidth theft”. Yes, theft. I have a hosting plan that gives me unlimited (nearly) traffic and bandwidth, so I don’t really have to care much about this anymore. Linking to an image is now allowed, but any kind of abuse will be fixed with a manual block of your site and its link, as the hosting company still can take my site offline if there is some kind of heavy traffic peaks. Always remember to give credit.

More on copyrights: according to modern copyright laws, everything one produces is already copyrighted as soon as it’s published, whether it has a copyright notice on it or not (of course, adding a © symbol gives a bit of help, some people can’t understand things if they aren’t explicit!). That means things cannot legally be used without permission from the authors, for any purpose, or at least this is how it should be. All of my artwork is copyrighted (yours too, if you have a website – even the ugliest animated GIF if YOU created it – not if it’s someone else’s work that was changed somehow – is your property). I also hold copyright to ALL my graphics, text, and HTML, except when noted. It doesn’t matter whether the person who uses someone else’s work would profit from that use or not (some people when taken to court claim that they didn’t want to make profit from that work, and that is sometimes true), using someone else’s work without permission is already a copyright violation, what matters is whether or not it is used with permission from the person who did it. There is a legal permission for that kind of non-profitable use (fair use), which doesn’t require a fee or a financial compensation for the usage, or things can just be discussed and an agreement can be made – again, ask me if you want to use anything for a particular reason that involves profit and money. I’m not that evil, if you follow the rules.

Please DO NOT post ANY of my images in places like Renderosity or similar communities. Once it’s there, you lose control of what happens to them (kind of the same as Facebook and Instagram, I suppose, but these art communities are… well… no, thanks).

Q: Can I add a link to your site?

A: Yes, of course. Use the link to the main page, using the following code (replace “your text” with any text you want to describe the links – I prefer you use the second option):

<A HREF=”http://www.fractalland.com”>your text</a>

<A HREF=”http://www.mundofractal.net”>your text</a>

Perhaps in the future I’ll make a banner if you just want to make a graphical link.

If you want to have your gallery page to appear on my fractal links page, just send me an e-mail with some basic info about your site and its URL. Sometimes I can add links to other fractal sites that might be interesting as well, trading links is always good.

Q: I am interested in getting some printed versions of your images, how can I do that if I can’t save them to my computer in high quality?

A: All the images on the site weren’t done thinking (at first, at least) of printing them by the visitors of the site, they were created for being displayed on the Web only, thus they have some degree of JPEG compression, size restrictions, etc. But they look great when printed in large sizes. But in order to do that, they need to be re-rendered with the proper settings for printing.

Images that are made for being displayed on a computer screen only have a much lower resolution than images that are prepared for professional printings (they have much probably just 72 D.P.I. while professional prints require at least 300 D.P.I. – although you can get some good results with a little smaller values), they have been converted to JPEG format most of the time, which is a format that causes some varying loss to the quality of the images. In some cases, the images were heavily compressed, to make them load faster, or to intentionally downgrade the printing quality.

Due to the nature of these images (they weren’t produced using a paint program like Microsoft Paint or Corel Photopaint or Photoshop or any other, but they are done by processing equations in the fractal generator software), it is possible to recreate most of these images to be professionally printed, at (almost) any size, in (almost) any resolution, using these same equations (this is called a “parameter set” – each image has its own, it’s like a recipe of a cake). If you are interested in purchasing a printed version of any of my images, just send me a message. I might be able to provide you with a printed version in a quality paper (glossy/photo) or directions for you to do it yourself using your preferred printing services, but I cannot do the framing/matting for you.

Q: Will you be making any of these “recipes” to recreate the images available?

A: No, no and no. If you want to share/get parameter files for Ultrafractal, Apophysis, JWildfire or Mandelbub 3D I suggest you try to join the UltraFractal Mailing List or some other community like Facebook groups about the specific software, in some of these places they allow sharing and even “tweaking” of the original parameters. I hate to tweak someone’s work (I’m destroying it!) and I don’t like mine to be tweaked just for the sake of it. More info about the UF list on the Ultrafractal resources page (I have no idea if it’s still available today, I unsubscribed ages ago).

With Fractint, a fractal generator (still for DOS), it’s possible to edit/rebuild the image if you load the image if it is in original .GIF format, but not in the GIF format that is currently used for Internet, Fractint uses an older GIF format to create the images (I open all my Fractint images in UltraFractal images to render them there). I still have a few GIF images, but if you try to load them in Fractint, they can open and be displayed but you won’t be able to edit them because they were saved in this newer GIF format and lost their “fractal” editing capabilities. I tried as much as possible to recover most of these images, opening them in UltraFractal, but some of them just didn’t work.

Q: Do you have any set of formulas for UltraFractal or other fractal softwares, written by you, that you could share with us?

A: No, I don’t have a clue about how to make these formulas nor do I have any knowledge about the math involved. I’m not a formula writer. I’ll probably add links to resources for all the softwares I currently use or have used.

Q: Have you been in any art exhibitions?

A: Yes, I was invited to my first exhibition, in Spain, some time ago (a long time ago, actually…). And I’ve also participated in another exhibition at the Lincoln Center NYC promoted by MOCA (Museum of Computer Art), which started January 3rd 2004. This art show was also extended to the city of New Jersey for more 15 days. Unfortunately, the links to these events have disappeared.

Q: Who is this Julia that appears here and there? Why do you talk so much about her?

A: She’s not a real person.