We here distinguish two different universes of drawings, each one having its own unique
properties: the universe of hand drawings and the universe of algorithmic drawings. In
each one we find good and poor works, but they all will display characteristics, which
definitely sort them into one or the other.
The universe of hand drawings contains all drawings made by artists since artists are
around (which is roughly 30,000 years). This universe has many departments: that of the
hastily produced sketches, that of carefully finished compositions, that of scientific
illustrations, that of the drawings of the human figure, that of the landscapes, etc. The
universe of the hand drawings is enormously rich. Its wealth is based on the power of the
human imagination, the sharpness of the eye and the motoric capacities of the hand.
Besides this universe there is a universe of algorithmic drawings. It is just as extensive and
impressive, like that of the hand drawings. ‘Algorithmic drawings’ are drawings that are
produced by strictly formulated rules.
The concept of algorithms is named after Abu Jaf’ar Mohammed ibn Musa al Khowarizm,
a Persian mathematician who published a procedure to solve quadratic equations around
the year 825. If we define a procedure as an instruction for acting, where at each step it is
clear what the next step will be, we can understand an algorithm as a procedure which
ends after a finite number of steps with a result. In computer programs, algorithms play
an important role and each program is itself an algorithm.
Sometimes artists decide to subject themselves to self-imposed restrictions that run close
to what is understood by a ‘program’ in information technology. Sentences like: ‘draw a
tree with short, violent strokes’, ‘use only vertical strokes of same length’, ‘go to and fro
along a contour’, etc., are examples for such ‘programs’. One can imagine the possibilities
over which the drawing hand can range as a continuum (see. Fig. 1, left side), which on
the one hand of the axis marks a strictly rule-guided use of lines, which is gradually
turning into a use of lines not following any rules at all and on the other axis a line, which
is gradually moving towards ‘painting’.
When we formulate rules for drawing by hand with increasing sharpness, we move
towards algorithmic drawing, and at some point cross the border separating both. Then,
we also find a continuum of possibilities (see Fig. 1, right side).
Interesting examples for the use of algorithms in the generating of drawings (and
paintings) by artists have been published by the artists of the renaissance in their struggle
to solve the problems of the perspective presentation. To construct the ‘correct’ perspective
image of a lute, Dürer has illustrated a procedure in the woodcut of
‘the draftsmen of the lute’ and gives the following ‘algorithm’: the
assistant strains a thread that runs through the picture plain
(represented by a frame, behind which the master is sitting) to a point
on the lute. The master mounts two threads to the frame so they touch
the tense thread of the assistant. Then the assistant loosens his thread,
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