Software

Anti-Aliasing
Anti-aliasing is the method of smoothing the edges of a pixilated object by blending a thin line of pixels along its edge with their surrounding environment.  Without it, objects in a visual field would appear to have rough, jagged edges.  Anti-aliasing is critical to fractal design, as it is predominantly a digital medium.  The problem is that the core makeup of most fractals is the infinite presence of points.  Areas of thinner density will often have stray points in open fields, and these points are usually overlooked by standard anti-aliasing.  Therefore, the concept of anti-aliasing for fractals takes on an additional dimension in that these stray points, otherwise referred to as “artifacts”, must somehow be visually diminished, smoothed, or removed entirely.  There are many methods for doing this, and they tend to vary greatly from program to program.  For the most part, though, these artifacts are removed through a process known as “oversampling”. 

Oversampling occurs when a program looks at multiple samples of each area of a fractal during the rendering process.  Each of these samples has a high likelihood of placing point artifacts in slightly different areas.  The software then uses these variances to determine the existence of an artifact and how it should be dealt with in the final render.  Depending on the software, it could choose to smooth the artifact into its surrounding pixels (much like anti-aliasing) or remove the artifact entirely. 

While anti-aliasing happens automatically and can be turned on or off by the user, oversampling is adjusted by specifying the number of samples that should be compared during the render.  The higher the setting, the greater the likelihood of determining the presence of an artifact, and the more information the software will have available to determine what should be done with it.  Unfortunately, each sample the program has to look at adds more time to the rendering process.  Some complex fractals can take hours to render even without oversampling, so it is easy to imagine how much more time a high sample setting would add.  If you can spare the extra rendering time, however, even a small sample setting can clean a finished render dramatically. 

Density Estimation
While oversampling is great for dealing with those pesky artifacts, there is still another related (and commonly overlooked) issue to attend to.  Areas of low to midrange density are made up of points as well, and the points in these areas are spread out and clearly visible.  These areas are dense enough to avoid being adjusted in sampling, yet sparse enough to create a noticeably grainy look in the final render.  Sometimes this grainy effect is preferable, but more often than not it is a nuisance.  Therefore, an additional filter is needed to polish these areas up a bit. 

Density estimation is essentially a dynamic form of blurring that targets specific levels of fractal density.  Since each fractal has a unique density map, and subsequently a unique level of low to midrange graininess, the optimal approach to density estimation will vary on a case by case basis.  Furthermore, few fractal design programs have a setting for density estimation, which means a creative alternative must be found.  In some cases, a fractal can be blurred based on its individual transformations (variations and effects that occur in layers or built-in incremental changes in a fractal’s script are often referred to as “transformations”).  Subtle blurring can be applied to transformations that will help to eliminate sparse point densities.  Care must be taken not to accidentally blur high density areas in the process, as these areas make up the primary details of a fractal.  Other programs have a filter radius setting for rendering that is very similar to density estimation.  Again, take care when setting these values.  Each fractal will require a unique and sometimes complex approach, but this process gets much easier with experience.  The results of good attention to density estimation will often mark the difference between a beginner and a seasoned pro.

The example below shows varying degrees of filtration applied to a simple fractal flame randomly generated in Apophysis. With no filters applied, the fractal looks extremely grainy. The default filtration settings do a remarkable job of cleaning up the render, but there is still a great deal of point noise. Optimal filtration was accomplished using a combination of the "filter radius" setting and targeted blurs. Finally, the over-filtered render was done using a high "filter radius" value, which subsequently invaded areas of high point density and ruined the detail.

No Filtration
Default Filtration
Overfiltered
Optimal

Example Blurs
Understanding Blurs

A blur is a method of smoothing pixels over larger areas.  Just as most graphic design programs utilize multiple different types of blur, so do a good many fractal design programs.  This is especially important for programs that work with variations based on point iteration, as these fractals are liable to look grainy in spots when they are rendered.  Skilled use of blurring not only helps to clear up these grainy areas, but can be used to add depth and finesse to a design as well.  The best part about fractal blurs is that they can be applied to the whole design or to specific transformations or functions within the design, the latter having any number of interesting outcomes.  While using blurs dynamically is an acquired skill, understanding what each type of blur does is important to any budding designer, regardless of whether or not they choose to work in a fractal-related genre.

Gaussian blur – This type of blur is smooth and even.  It moves in all directions, from all directions.  A low setting would create a subtle, 1-pixel blur, while a high setting would likely render the whole affected area unrecognizable.  Unrecognizable, but smooth… very, very smooth. 

Radial blur – A radial blur differs from a Gaussian blur in that it moves outward in all directions from a single point.  This blur is most effective when trying to create an illusion of motion zooming in and out.

Directional blur – This blur moves from a line or point of origin in a single direction.  It is useful for creating the illusion of movement for a single object going in a single direction.

Motion blur – This blur is bidirectional, which means it extends in two opposite directions, usually left and right or up and down, but could be done diagonally as well.  The movement occurs not from a point of origin, but rather from all points in the affected area.  This type of blur is most commonly used at small settings to create the illusion of vibration, or at larger settings for more surreal effects.