5. Fractal art information 

Table of contents

 5A. Computers and colors

 

 5Aa. 

What are color models? 

 

 5Ab. 

What is the RGB model? 

 

 5Ac. 

What are the HSV and HSL models? 

 

 5Ad. 

What are the CMY and CMYK models? 

 

 5Ae. 

Do I see the same image as the artist who has created it? What is gamma? 

 

 5B. Making images 

 

 5Ba. 

How are the colors of fractals obtained? Basic information. 

 

 5Bb. 

What is the escape time method? 

 

 5Bc. 

How to smoothen the repartition of colors? 

 

 5Bd. 

What are orbit trap methods? 

 

 5Be. 

What are height field fractals? 

 

 5Bf. 

What is aliasing? 

 

 5Bg. 

How can I anti-alias images? 

 

 5Bh. 

Can I take photos of the screen? 

 

 5Bi. 

How can I get high quality photographic prints of my fractals? 

 

 5Bj. 

How can I make prints of fractals with my color ink-jet printer?

 

 5Bk. 

How can I get high quality paper prints of my fractals?

 

 5Bl. 

How can I learn to obtain good images?

 

 

 5C. Fractal images on the web 

 

 5Ca. 

Where can I find fractal galleries on the web? 

 

 5Cb. 

To which newsgroups are fractal images or information posted? 

 

 5Cc. 

How can I see images in those newsgroups? 

 

 5Cd. 

What is the fractal art contest? 

 

 

 5A. Computers and colors 


 5Aa 

What are color models? 


   Colorimetry and photometry are sciences dealing with somehow complex concepts and vocabulary. But it is not necessary for our purpose to understand what exactly are luminance, lightness, brightness or chromaticity and purists may object that I will sometimes use words with a meaning which does not exactly match the official definitions. You must just know that there are several conventional systems to quantify the distribution of colors in an image. These systems are named color models, or colorspaces. According to the technique used to create or reproduce the images it is necessary to choose the model which best fits the characteristics or limits of the technique. A minimum knowledge in this domain is useful to master the use of colors in fractal images.

   For more information


 5Ab. 

What is the RGB model? 


   The most well known model is the RGB (Red-Green-Blue) one. All the colors can be obtained by blending various amounts of each of these 3 basic colors. This system is used by TV cathode ray tubes and computer monitors. Each pixel is made of 3 small adjacent phosphors emitting respectively red, green and blue lights when excited by the electron beam. This model is said additive because each color is obtained by adding the lights emitted by each phosphor. For example equal values of red + green give yellow. In computer images, the best that can be done is to code the intensity of each color on one byte. Therefore the emission of each phosphor can have 256 distinct levels (from 0, for black, to 255 which is the maximum of emission for this color). Each pixel being made of 3 phosphors, this technique allows the coding of 2563 = 16,777,216 colors. This mode is usually named: 16 millions of colors, true color or 24 bit color mode.
   You must understand that an image can’t have more colors than the number of pixels (480000 for a 800x600 pixels image). You must also understand that if you only use one color to create a monochrome image (for example pure blue), you can have only 256 shades. It is the same if you create a black and white image.
   Everybody knows that the eye has not the same sensibility for all the colors. It is why blue = 255 appears several times darker than green = 255. Indeed pure blue is not very bright and a pure blue figure on a black background looks poorly contrasted. But the most luminous yellow that you can obtain is made of red = 255 + green = 255. Therefore mixed colors can be more luminous that pure ones.
   Nevertheless this technique gives the best possible results in almost all the usual cases. It can give very vibrant as well as pastel-like colors.


 5Ac. 

What are the HSV and HSL models? 


   HSV and HSL (or HLS) colorspaces are practical models which are not related to any specific material. They use the hue (H) system to code colors. To understand hue let imagine a circle where red is at position 0°, green at position 120° and blue at 240°. Obviously, by a rotation of another 120° step, you come back to red (because 360° points to the same  position as 0°). Now let imagine that between each of these points you do a progressive blend of the two adjacent colors. You observe a continuous transition between all possible colors (with yellow at 60°, cyan - a sort of light blue - at 180°, and magenta - a sort of purple - at 300°).
   Saturation (the S component) is, roughly speaking, the inverse of the amount of white added to the color (that is when S = 100% no white is added to the color; for example pink is an unsaturated red).
   But the two models differ on the third component.
   V, for value, is a measure of the brightness of the color. For example a pure red 255 is H = 0, S = 100%, V = 100% (when these parameters are coded on one byte, you may find 255 instead of 100%). When S = 0 and V = 100% you obtain white whatever the starting color (hue) is.
   On the contrary L (lightness) behaves in a different way: pure red 255 is H = 0, S = 100% and L = 50%. Between 50% and 100% you add white to the color: for example H = 0, S = 100% and L = 75% correspond to R = 255, G = 127, B = 127. When L is 100% you get white, whatever the color chosen for hue. Therefore L interferes with S for L > 50%. Here again you can find 255 in the place of 100%.
   Most of the fractal programs use the RGB model to define colors but, in addition, some of them can also use the HSV model (Fractal Zplot) or the HSL one (Ultra Fractal). These two models are very useful to build gradients in palettes used to color the fractal images (HSV, in my opinion, is the most intuitive one). But in all the cases the program must translate the H, S, V or L parameters to RGB, which is the only system used by graphic cards and computer monitors.

   For more information


 5Ad. 

What are the CMY and CMYK models? 


   It has been emphasized above that the RGB model is additive. It is well adapted to situations like computer screens because the screen emits its own light. But can’t be applied to printed images. This can be explained easily. When an image is printed we start with a white sheet of paper and we print a colored dot: it absorbs the light in a given range of wavelengths; now we print another dot of another color: it absorbs light in another range of wavelengths. You see clearly that the printing of an image is a subtractive process. Another color model is needed.
   It is the case of the CMY (cyan, magenta, yellow) colorspace. Basically printers use 3 inks of the colors listed above. Cyan absorbs red wavelengths, magenta absorbs green and yellow absorbs blue. If an area is totally covered by an equal deposit of the three inks it must look black (the subtractive process) and by controlling the amount of each ink (printed as dots on the paper) it is possible to reproduce all the colors.
   Well, that is the theory but in the real world there are some drawbacks. First of all the CMY colorspace can’t cover the whole range or colors and brightness which can be obtained by the RGB technique. This is why images with very saturated colors and high contrasts look often somehow disappointing when printed on paper. Secondly real pigments are not perfect: for example cyan mainly absorbs red, but may also absorb a small amount of other wavelengths. This explain why some shifts in colors are observed. Indeed if you try to obtain black by mixing the three CMY inks, the result is a dark brown. This problem has been known for a long time and is corrected by the addition of a fourth ink, black, which can be mixed with the three others to obtain darker colors. This technique is known under the name of quadrichromy, or CMYK model and it gives very good results in classical printing.
   These shifts of colors are much more difficult to correct with inkjet printers because inks are very different from those used by classical printers. Most of the inkjet printers use inks which are colored solutions. Some expensive inkjet printers can use two more cartridges of special inks for more photo realistic results but this may not be enough to render some fractal images. A few printers use inks which are suspensions of pigments. These inks are expected to be more stable and can give more saturated  colors.


 5Ae. 

Do I see the same image as the artist who has created it? What is gamma? 


   This question is not trivial. It is obvious that the rendering of an image depends on the settings of the monitor. The two common controls are contrast and brightness and it is strange to observe how the settings that peoples judge to be optimum are different. These parameters have a great impact on the rendering of the images. Moreover, different monitors may exhibit a few discrepancies in the balance of the three RGB colors, introducing some shift in colors. These shifts may increase with the ageing of the monitor but this problem is negligible with good monitors.
   These problems are objective. But subjective influences may have a great impact on the final perception of the image. Subjective brightness, contrast balance of colors are largely dependant of the ambient light, the color and brightness of the background (that of the wall behind the monitor in most cases). For example it is well known that our brain is able to build a subjective reference white from information coming from the environment, to  partially compensate differences of illumination. It is why a white object appears white, and why colors are rather identical, under sun light or under artificial (tungsten) light . But if you use a daylight slide film to photograph a scene illuminated by tungsten bulbs the transparency will look yellowish because the film does no compensation.
   The drivers of some graphic cards (or the monitor itself) have settings to change the equilibrium of the colors of the screen. This may be useful when you display photographs on your monitor because you know what the usual colors of the sky, the skin, the leaves, etc. are, but this is of little use with fractal images which have arbitrary colors. However this may help if your monitor has an obvious shift in the balance of colors.
   However an underestimated problem is the fact that approximately  8% of the male population suffers from dyschromatopsy, a term which covers various trouble of color vision (known in French as “daltonisme” because it was first described by the great chemist Dalton). Strangely enough some known painters suffer from this trouble.
   But there is another problem which is specific to the type of computer used: the gamma of the monitor.
   The problem of gamma has been studied first for TV images. It is related to a physical property of the electron gun used in cathode ray tubes (CRT). The intensity of the light emitted by the point excited by the electron beam is not proportional to the input voltage of the gun: it is proportional to Vg (Vgamma) where gamma = 2.5 for most of the CRT. Therefore an input voltage of 50% produces an intensity of 18% (point A of the curve).
   The problem shows some other complications because the range 0-255 is not exactly enough to cover the range of what can be distinguished by the eye. To correct this problem computers use color translation tables (or lookup tables) to convert the value of each byte to the adequate voltage. For the PCs these tables don’t take into account the gamma problem. It is why the gamma of a  PC monitor is always very close to 2.5.
  And here is another cause of dispute in the holy war between supporters of PCs and supporters of Macintosh. The translation tables of the Macintosh introduce a partial correction for gamma and the Macintosh displays have a gamma of 1.8 (this value is close to the gamma of laser printers and this explains why halftone images look quite similar on a Macintosh display and on a printed document).
   The problem is that images created with a PC have not the same rendering when displayed with a Macintosh and vice versa. Because of the concavity of the curve mid tone values are more affected than dark and light ones. For example the screen of a Macintosh emits with an intensity of 29% for an input voltage of 50% (point B).
   The global result is that the mid tone areas of an image made with a PC appear lighter on a Macintosh display, and they appear darker when they have been created with a Macintosh and are displayed with a PC. Moreover this problem causes some shifts in colors for reasons not necessary to explain here. Note also that some graphic oriented workstations use a gamma of 1, but most of the fractal images are made with PCs and some others with Macintosh.
   There is no general solution to this problem because JPEG coding of images doesn’t record any information about the gamma used when the image has been created. PNG format can record this information but, for what I know, web browsers and many usual graphic programs do not use it to adapt the rendering of the image to the gamma of the computer. Some graphic cards for PCs have a driver which can modify the gamma and this can be used if the origin of the image is known.

   For more information

 

 5B. Making images 


 5Ba. 

How are the colors of fractals obtained? Basic information. 


   This is the secret of the complex polynomial fractal images. The most interesting zones are on the external margin of the set. We know that none of the points of the complex plane behave in the same way when iterated. This behavior can be characterized by several mathematic properties but, whatever the property chosen is, it is possible to represent this behavior by a number. If we have a series of colors, generally known as a palette, each number can correspond to the rank of one color on the list. That color will affect the pixel representing the point.
   What happens if the computation results in a number greater than the number of colors in the palette? Suppose that we use 256 colors. If the value to display is above 256, the program restarts with color #1 (in other words, colors are applied modulo 256).
   The beauty of images relies on the choice of colors on their palettes. Generally these palettes contain several progressive gradients of colors to obtain aesthetical patterns in the fractal image. You can now understand that these gradients may be based on hue (color), saturation or value (or lightness). When using gradients based on transitions between two colors, pay attention to the fact that some transitions may give “muddy” colors.


 5Bb. 

What is the escape time method? 


   The escape time method is the most classical and oldest to color fractals. It is based on the answer to the question: after how many iterations can you see that the point does not belong to the set (a point does not belong to the set if the orbit tends towards the infinite)? If you detect that the orbit “escapes” after n iterations, give to the point the color of rank n in the palette.
   If need be, you can merely use black and white -- one for even values and the other for odd ones -- to get and idea of the distribution of the values, but results are more aesthetical with a polychrome display (after the 16 colors of PC’s old VGA, the 256 colors mode imposed its standard, and was popularized, in particular, by Fractint; more recent programs can use an almost unlimited number of colors). Observe that the points are distributed into “concentric” zones around the area corresponding to the set itself. The zones are tighter and tighter as you go closer to the set.
   Realize that it is not the value reached by the function for the latest iteration which is displayed by this method, but the number of iterations needed to see that the orbit escapes. Each number is used as in index related to one color of the palette.


 5Bc. 

How to smoothen the repartition of colors? 


   Regardless of the skill to build a palette with uniform shade repartitions, discontinuities are generally clearly seen between successive colors in fractals made with programs using 256 colors. Programs using more than 256 colors are a must to allow smoother transitions between adjacent colors.
   Anyway, it is not enough to have a program handling colors with 24 bits (true color mode) to have smooth color transitions: the algorithm that computes the fractal also needs to provide adequate values. In the classic escape time method, it is impossible to have a number of colors greater than the maximum number of iterations chosen for the calculation. And yet the computation is generally limited to one or a few hundreds of iterations owing to the length of the process. It is an intrinsic feature of this algorithm to give discrete areas of colors. 
   Fortunately the number of iterations necessary to detect the divergence is not the only result which can be used to fix the color of a point. Every algorithm giving progressive fractional values is a good candidate for a true color rendering. Linas Vepstas has described an interesting algorithm giving a progressive variation of colors by modifying the escape time method. Basically, its principle is to compute, not only the number of iterations needed to detect the divergence, but how distant the point is from the limit between two successive iterations as well.

Other methods, known for a long time, may also be useful. For example we can use the angle made by the orbit with the x axis at the time when the divergence is detected. Or again we can use the potential calculated by the formula log|z|/2iterations, providing that a very high value is chosen to test the divergence.
   From a more general point of view, we have seen that the classic method uses the number of iterations and not the value of the function when the orbit escapes. But the value of the function or any value derived from it can be used to assign the color: for example, you can use the real part, the imaginary one or any composition of them. You can combine these values with the values of the preceding points of the orbit, or with the number of iterations... The numbers obtained during the calculation can be transformed by using varied functions (log, exp, trigonometric functions, Boolean functions...).
   Take into account that, in the previous description, only the colors of the points outside the set have been discussed. All the points of the set are displayed with the same color (blue in the default palette of Fractint, but it is only a matter of convention). Indeed the points belonging to the set are not identical because the results of the iterations of the function draw an orbit restricted to a portion of the plane, which is different for each of them. Therefore, this numerical information can be used to allocate distinctive colors to those points and then to observe colored structures into the area corresponding to the set itself.


 5Bd. 

What are orbit trap methods? 


   It has been assumed that the criterion used to color the point was only determined by the detection of the divergence of the function. Some specialists on fractal images have imagined more subtle methods.
   A fractal rendering method was developed by Paul Carlson in 1994 that was known as the 3D Stalks Method. That rendering method was the forerunner of several other fractal rendering methods developed by Carlson which have become known as “orbit trap” rendering methods, so named because during the iteration of a complex function the value of the function moves to different points in the complex plane, tracing out an “orbit”.  An orbit trap is a closed area in the complex plane into which an orbiting point may fall.  The principle is to test, for example, if the orbit of the point falls into a circle, an annulus, a square, et cetera. When this occurs, the point is considered to be “trapped” and the iteration loop is exited.  The distance from the orbit point to the center of the area is then computed and divided by the maximum distance from the center of the area to the area boundary.  The resulting ratio, which is always less than unity, is converted to an index into the colormap in such a way that ratios near zero  will index to a bright intensity of a hue, and ratios near unity will index to dark shades of the hue. This method gives the elements in a fractal image a rounded, 3D appearance. The resulting images show fractal structures made of spheres, annuli, cylinders, cones with a very “solid” appearance.
   These techniques are now incorporated into several fractal generators.  Phil Pickard has greatly contributed to this with his personal algorithms and by sharing his program Fractal Orbits (see 6g). This program was the first to enable non-programmers to create images using orbit trap techniques. Later on Terry W. Gintz has incorporated these methods in his programs and  Paul Carlson, Damien Jones and others have adapted these algorithms to Fractint and Ultra Fractal. During year 2000 Paul Carlson has made available the program Mind-Boggling Fractals (see 6g).   


 5Be. 

What are heightfield fractals? 


   As has been stated above, it is possible to represent some property of the behavior of each point by a number. So each point is defined by 3 coordinates: the real and imaginary parts x and y, and the number representing the behavior of the point (which is usually coded as a color). It is also possible to use a 3D visualization, this number being the height of the point, providing that the position of the observer is specified. This can be combined with the use of a color map and ray tracing.

 

Height field rendering of the Mandelbrot set


 5Bf. 

What is aliasing? 


   Aliasing is a by-product of the discrete sampling employed by the computer. Because of the finite resolution of a computer screen, a single pixel has an associated width, whereas in mathematics each point is infinitesimally small, with no width. So a single pixel on the screen, computed for a single point, actually covers an infinite number of mathematical points, each of which may have a very different correct visual representation.
   Fractals are very strange objects indeed. Because they have an infinite amount of arbitrarily small details embedded inside them, they have an infinite number of frequencies in the images. When we use a program to compute the image of a fractal, each pixel in the image is actually a sample of the fractal. Because the fractal itself has arbitrarily high frequencies inside it, we can never sample high enough to reveal the “true” nature of the fractal. Every fractal ever computed has aliasing in it and every pixel may be a false representation for many mathematical points of the area it covers.
   Aliasing is responsible of the jagged appearance of the limits of areas of different colors, of the coarseness of images in areas of complex structure, and of the moiré pattern often seen in parts of the images having very tight fractal periodic structures.


 5Bg. 

How can I anti-alias images? 


   We can’t eliminate aliasing entirely from a fractal, but we can use some tricks to reduce it. This is what is called “anti-aliasing.” The technique is really quite simple. We choose the final size of the image and take a sample at a higher resolution than the final size. So, if we want a 800x600  image, we use at least 3 times the number of pixels in our “super-sampled” image - 2400x1800, or more, for even better results.
   But wait, we want a 800x600 image, right? Right. So far, we haven’t done anything special. The anti-aliasing part comes in when we take our super-sampled image and use a filter to combine several adjacent pixels of our super-sampled image into a single pixel in our final image. In other words, we replace several pixels by one which is a weighted average of the grouping. The selection of the filter is very important if you want the best results! 
   Most image manipulation and paint programs have a resize function with anti-aliasing option (in some programs the option is named “resample”). You can try this and see if you like the results. Unfortunately, most programs don’t tell you exactly what filter they are applying when they “anti-alias”, so you have to subjectively compare different tools to see which one gives the best results.
   The most common and widely implemented filter in graphics programs is a simple averaging of neighboring pixels in the super-sampled image.  Unfortunately it gives poor results. Unless you are a programmer, your best bet is to take your super-sampled image and try different graphic programs and filters to see which one gives you the best results. But, if you can choose the filter in your graphic program, note that the Mitchell filter is one of the best. Anti-aliased images are generally too soft but they can be improved by the use of a slight sharpening filter.
   Many fractal programs now incorporate anti-aliasing directly in the fractal generation process along with a good quality filter.


 5Bh. 

Can I take photos of the screen? 


   Taking photos on screen of fractal images is not the best method but it is easy to do and gives acceptable results for modest enlargements.
   Use 200 ISO (ASA) film for prints or for slides. Use a long focal lens (100mm) to flatten out the field of view and minimize screen curvature. Use f/4 stop or more. Shutter speed must be longer than frame rate to get a complete image; 1/4 seconds is the minimum. Use a tripod and cable release or timer to get a stable picture. The room should be completely blackened, with no light, to prevent glare and to prevent the monitor from showing up in the picture. Use full screen display of the image (image size of 800x600 is the minimum; more is desirable). A large size screen will minimize the size of pixels on the print. It is suggested to reduce the contrast of the screen and perhaps to change the balance of colors if this option is offered by your graphic card. Some tests are required because these parameters are dependent on the screen and film used.


 5Bi. 

How can I get high quality photographic prints of my fractals? 


Prints from Film
   These prints are the most like traditional photographs, and require either a negative or a transparency of the image. The transparency (typically a slide) is a positive image; looking at the slide shows you the same image as you saw on the monitor. Negatives reverse the color, so something that was blue on the monitor will be orange on the negative. The advantage of using negatives is that they can be printed by any “one-hour” minilab. Transparencies, on the other hand, can usually only be printed by a photo lab. However, the quality of a good print directly from a transparency far exceeds that from a negative provided  Ilfochrome Super Gloss paper (known for a long time as Cibachrome) is used (and perhaps a few others like Fuji Super Gloss reversal paper), but these prints are expensive. Prints from transparencies made on usual papers give generally poor results.
   For quick, inexpensive prints, photographing the monitor is one option, and you can use print or slide film. For higher quality negatives or transparencies, consult a service bureau or a professional photo lab. A photo lab will use either a film recorder or a digital imaging system to expose the film. A film recorder is essentially a high quality monitor on which the image is shown, and then photographed. The digital route typically involves your providing a high-resolution render of your fractal image to the service bureau which will then use a machine like the Kodak LVT.  The LVT uses lasers to expose each pixel of the image directly onto the film, without using a monitor. Consequently, LVT films can be of higher resolution than recorder films, and suffer no distortion due to the geometry of the monitor.
   Once you’ve gotten your film exposed and processed, you have to entrust it to a photo lab for printing. Unfortunately, this step is critical to getting good prints, and is one over which you may have relatively little control. It will be important to find a photo lab with whom you can work and who will take direction. If possible, you should have a color guide to show the printer how the colors should look.

Low(er) Cost Photographic Prints
   We have found websites from which you can order prints of your digital images on photographic paper. A web search on “digital photography labs” should turn up several. Some of these websites offer online albums from which your friends and family can order copies of your prints and at least one offers greeting cards and other gift items emblazoned with your images.

Archival Quality Digital Photographic Prints
   In this method, lasers directly expose the photographic paper without any intermediate film. The final print quality compares favorably with traditional photographs, and the print lifetime should also be many decades. An advantage of digital prints is that a negative or transparency is not needed.  Current machines print at 200 dpi, which means that your print will have a maximum of 200 pixels per inch, but because the paper is exposed with continuous tone rather than dots, this produces a beautiful print. Newer printers reportedly print up to 400 dpi, but, according to Damien Jones the difference at 400dpi is very slight.


 5Bj. 

How can I make prints of fractals with my color ink-jet printer? 


   If you’re going to be printing your images on your home color printer, you’ll need to generate an image that is 300 dpi — that is, you want 300 dots per finished image inch. For an 8” x 10” finished image, your rendered image needs to be 2400 x 3000 in size. If you use anything less than 300 dpi, you are likely to see quite noticeable pixelation (dots) in your print. You will probably want to print the image using your printer’s highest dpi setting. Be prepared for a small to fair amount of color inaccuracy, specially for saturated colors, with these kinds of prints because inkjet printers use the CMYK colorspace (see 5Ad).
   Some adjustments in color, brightness, contrast, etc. can be made with your printer software and in your graphics program. Each printer is different, so be prepared to experiment to find out what settings work best for you. However these prints generally fade with time, specially when exposed to bright light.


 5Bk. 

How can I get high quality paper prints of my fractals? 


Giclee Prints
   “Giclee” is from the French for “spray”, and giclee prints are essentially ink jet prints. The most famous trade name is Iris, and the phrase “Iris print” was synonymous with “gallery quality prints of digital art”. The inkjet technology for giclee prints is quite sophisticated, when compared to typical desktop inkjets. Giclee printers are relatively slow, and are not well suited for high-volume applications. They print one sheet at a time, and sheet sizes are typically limited to 35 inches by 47 inches. This apparent limitation is offset by the fact the giclee printers can use a variety of papers, from smooth surface coated papers to watercolor stock.  An open question in the digital art community concerns the stability and longevity of the prints. Before investing in a giclee print, be sure to discuss this issue with your printer.


 5Bl. 

How can I learn to obtain good images? 


   What follows can only be considered as suggestions.
   First, look at numerous fractal galleries on the web (and other sources of images given in this FAQ) until you identify styles of different artists (but one artist may have images of different styles) and  until you feel that you want to do a certain style of images.
   Look at sites where formulas are provided (a considerable number of formulas are also published in the Fractint and Ultra Fractal mailing lists; many artists publish parameters which allow you to redrawn their images). Start with a formula and parameters which correspond to an interesting image and try to see how the artist has obtained the final result. To do this you can zoom out to identify in what zone of the fractal the image has been selected. Look at the color palette and try to modify it.
   Try to change slightly some parameters in the formula. Try also to modify the criteria used to color the image (it is not easy to give explanations which apply to every program because, beside some general features, each program has specific features and uses its own menus and vocabularies). By doing that on a number of images you can discover some interesting information and, moreover, you can also create, with this method, original and very interesting images.
   Then, try to do something yourself. The best way is to start from a rather simple formula (there are very complex ones but the more complex a formula is, the more difficult it might be to control how changes in parameters affect the result). Make the greatest possible number of images: many of them will be thrown in the trashcan later but it doesn’t matter for a first time. Work and work again on this formula until you discover what zones of the fractal give interesting results, till you can master the results and perhaps predict them to some extent.
   It is not a good tactic to flit from one formula to another. If you have a good familiarity with a formula you will be able to obtain a great number of very interesting images. Some artists have created large series of very different images based on one formula or a few variation around the same basis.
   Don’t be discouraged if for some days (or some weeks) you can’t get any interesting results: some artists are very prolific, but many others know these periods with lack of inspiration or results.

 

 5C. Fractal images on the web 


 5Ca. 

Where can I find fractal galleries on the web? 


   There is a significant number of outstanding or very good fractal galleries, so it would be unfair to give a limited list. The Infinite Fractal Loop is a site having the greatest number of links to galleries. All these galleries are linked together:

   Some other fractal web rings are listed at

   When you visit a gallery look at the links chosen by its author: you will see that some of them are very often cited. Experience tells us that the most quoted and listed galleries are the most outstanding, in general terms. But there are some people that won’t like this point of view, because each person has his or her own criterion of selection of what he or she likes or dislikes, while some others could be discouraged.


 5Cb. 

To which newsgroups (and web groups) are fractal images or information posted? 


   The interest of newsgroups dealing with fractal images and related information is that you can publish your images for the public to see even if you don’t have a web site. Many artists have begun in alt.binaries.pictures.fractals (abpf). If you see that your images are appreciated, you may wish to have your own web gallery later.
   The availability of the following newsgroups will depend on the usenet groups available on your server.

   Most frequent for image posting:

   Most frequent for information:

   A group created more recently (December 2000), but doesn't show in many newsgroup servers yet:

   Other groups

   Yahoo groups (web groups): the most active for image posting are

   Other yahoo groups can be found by using the keyword fractal to search them.


 5Cc. 

 How can I see images in the newsgroups? 


   There are specialized programs that work as standalone news readers. Purists think they are the best solution. It is probably true, but probably most of you use integrated programs. If you use Netscape Communicator, a news reader is included (see the menu “Communicator”), but if you have Netscape Navigator 4 Standalone only, you don’t have the news reader. If you use Internet Explorer, your mail reader is probably Outlook Express. This program is also a news reader.
   In any case, you must specify in the settings the name of your news server. It is generally something like news.domain-of-your-ISP.com
Then you must select the groups you wish to “subscribe” to. There must be an option to select groups of interest (because your news server can probably offer you thousands of groups). You do this by typing the name fractal in the appropriate field: the list of all the groups containing fractal in their name will appear. Now, select the groups you are interested in. They will appear automatically every time you open the news reader.
   Modern news readers automatically decode the images attached to the news messages. If you want to send an image to a newsgroup (you must not send images to groups which are not interested in accepting them), it must be attached to the text of your message (with Outlook it is exactly the same thing as attaching a file to a mail).

   Important warning: When you send a message to alt.binaries.pictures.fractals, the title must contain a  keyword such as “fractal”, “Mandelbrot” or “Julia”. If you omit the keyword, your message will be automatically deleted during the process of diffusion to other servers (you will not see the problem because the message appears on the server of your ISP). Note also that it is best to use the Uuencode encoding for the images because it is a standard in picture groups. Other encoding like base 64 (Mime) or Binhex are not decoded by some programs.
   Read carefully the abpf FAQ for more information. It is posted each week in the abpf newsgroup.


 5Cd. 

What is the fractal art contest? 


   In 1997, a Fractint contest of fractal images was started in the Fractint mailing list. In 1998 and 1999, contests opened to fractals made with any program were initiated in the fractal art discussion list. The Fractal Art contest was managed by Damien Jones and was open to every artist, whether a member of this list or not (but the preliminary discussions and elaboration of rules have taken place in the discussion list). Entries were anonymous, and everybody could vote for best images in several thematic categories.
   The Year 2000 contest sites are:

   No Fractal Art Contest has been organized for 2001, Damien having no enough time to manage it.

   Images of the previous contests can be seen at:

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