Algorithmic Art would be the art for creating images with the help of (computation) algorithms. It can be understood in a very strict sense, as algorists do, by forbidding any not algorithmic intervention, or in a more relaxed manner, by tolerating a post-processing through graphic software, or through photomontage techniques (as is the case for my Markus-Lyapunov pictures). It is obvious that no artistic school can keep its boundaries closed for long and that somebody will, ever, appear to mix the styles.

A pionneer, Yiochiro Kawaguchi, is still winning recent competitions with his pictures.

Not all the pictures are fractal. Fractal techniques are often used in the background in order to give complexity to pictures, but other techniques are possible (such as the plotter images of Roman Verostko or the plane mappings of Escher). On the other hand one can also prefer a minimalist zen-like simplicity (for instance, see Jean Pierre Hébert).

The algorists do not recommend any artistic style or any digital technique (moreover, they admit non-numerical algorithms). They insist upon obtaining artworks in a pure algorithmic way, with no post-processing. The result can be an image as well as a sculpture, or even an ephemeral drawing on the sand! They consider algorithms an important part of the originality of the work, which makes me doubtful. If one admits that the public must be able to appreciate an artwork with no special information about the author, all these requirements on the creative process look excessive, as would be any ban on mixing various pictural techniques.

The algorithmic pictures are not limited to fractal pictures like mines or Fractint-like pictures. They include

• visualizations of classical computations, such as the rendering of "classical" surfaces (i.e. non fractal) computed with software like Mathematica or Mathlab. As an example, see the minimal surfaces of Helaman Ferguson or Séquin and Collins (IEEE Computer Graphics and Applications, November 1998, pps 15-20);
• the fractal landscapes of Kenton Musgrave, far more complex and realistic than what can be achieved so far with the popular commercial landscape generators. Kenton Musgrave attaches a great importance to the algorithms that were defined by himself or his students, and he defines himself as an algorist. However, since he has now joined the design group of Bryce, these algorithms might become a part of a future super-Bryce, and that an artist could use them unknowingly. Where will go the future artworks produced in this way, when compared to those of Kenton Musgrave?
• the genetic pictures are obtained through a succession of mutations of an initial image, following selection rules inspired by genetics. The reference names are Karl Simms and Steven Rooke, but Kenton Musgrave also did preliminary attempts in this field.
• Lastly, one can build abstract virtual sceneries with the help of 3-D software and render them as abstract pictures (through ray-tracing, for instance), quite as attractive as our fractal pictures. One can get "purely" algorithmic pictures by controlling the 3-D modeler automatically, but one can control it "by hand" as well, just as a virtual sculptor; it could be difficult to perceive the difference on the final result. I believe that the pictures of Yiochiro Kawaguchi belong to this category, and also those of Robert H. Russ (IEEE Computer Graphics and Applications, March 1995, pps. 4-6)