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## CODING DRAWINGS BY CIRCLE NUMBERS

There are many straightforward schemes for encoding drawings generated by Rules 1-6. Referring again to Fig. 1, let us define the radius of the initial circle (the frame) as 1. A visible circle is any circle wholly or partly covered by the initial circle. Starting with the initial circle, we generate all visible circles; each is given a number. The initial circle is given the number 1. There are 12 visible circles with radius 1 intersecting the initial circle. They are numbered 2, 3, . . . , 13 (in some deterministic fashion--clockwise, for instance). There are 31 visible circles with radius 0.5 (partly) covered by the initial circle. They are numbered 14, 15, . . . , 44, and so on.

Obviously, there are few big circles with small numbers. There are many small circles with large numbers. In general, the smaller a circle, the more bits needed to specify its number.

An unshaded drawing is specified by a set of legal arcs (forget Rule 6 for the moment). For each legal arc l, we need to specify the number of the corresponding circle cl, the start point sl, the end point el, and the line width wl. By convention, arcs are drawn clockwise from sl to el. Once we know cl, we can specify sl by specifying the number of the circle touching or intersecting cl in sl. In general, an extra bit is necessary to differentiate between two possible intersections. Similarily for el. Thus, all ``pixels'' of a legal arc may be compactly represented by a triple of circle numbers, two bits for intersection differentiation, and a few bits for the line width.

Clearly, the larger the circles used, the fewer the number of bits needed to specify the corresponding legal arcs and the simpler (in general) the drawing. By using very many very small circles (beyond the resolution of the human eye), anything can be drawn (using Rules 4 and 5) so that it looks ``right." This would not be very impressive, however, because a lot of information would be required to specify the drawing. It would be more impressive if it were possible to draw something non-trivial that looks right using only legal arcs defined by a few large circles. In a way, this would be related to capturing an object's essence, provided one agrees that the essence of an object is inherent in the sortest algorithm describing the object. Such compact representation can be difficult, however. I found that it is much easier to come up with acceptable complex drawings than with acceptable simple drawings of given objects.

Why use fractal circles instead of fractal squares? Since I prefer to sketch living objects as opposed to inanimate objects, and since I found it hard to convincingly sketch living objects without using curved lines of some kind or another, I decided to use circles as a basis for my fractal scheme.

Often the low-complexity artist will use drawing-specific symmetries and the like to further compress the description of a drawing. The next section will present examples of this.

Next: EXAMPLES OF CARTOONS BASED Up: FRACTAL CIRCLES FOR CODING Previous: Comments
Juergen Schmidhuber
1998-06-04

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