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'Painting by Functions' printed from http://nrich.maths.org/
In minimalist, abstract or computer generated art a real object is
often represented by a simplified set of shapes and curves.
For example, this image of the famous artist Mondrian might be
transformed or represented by transformations of standard
mathematical functions as follows:
Consider some objects and works of art. Think how they might be
broken down into shapes or segments of lines and curves. How many
such shapes or line and curve segments would be needed to give a
recognisable abstract impression of the pictures? Imagine how you
could encode your lines and curves mathematically by imposing a
coordinate grid on the picture.
Use a graphing software package to create your impressions
mathematically. Your toolkit contains the standard mathematical
functions: Polynomials, sin, cosh, sinh and also the techniques of
composition and transformation of functions.
You might want to print off the picture, highlight the segments of
the curves of interest and colour according to the colouring
schemes in Painting by
Please send us any of your creations!
If you want to focus on pictures made with straight lines, see the
problem Painting Between The
NOTES AND BACKGROUND
The mathematical issues raised in this problem are directly related
to the creation of computer generated art where images are
typically encoded mathematically; indeed if you zoom in closely to
any digital image you will see that it is encoded as squares or
blocks of uniform colours which give the impression of an analogue
In computer gaming, images are first represented minimally and
digitally using mathematics; the next phase is to animate the
You can read more about the mathematics of art on the Plus website
by Lewis Dartnell
package: Maths and art
contains many fascinating links and