ArtGraph is a computer program that I began writing in July 2004 to
visualise mathematical equations as Modern Art.
An ArtGraph is an image from this software.
The images are created from mathematical equations but are coloured
independently of the equation as is the whim of the composer.
The equations can be as simple or, within reason, as complex as desired.
I can best start to give a feel for what working with ArtGraph is like by
talking about some of the images I've created using this software.
The ArtGraph shown above arises from the simple equation
x 2 + y 2 = 8 sin ( x 2 + xy + y 2 )
The x 2 + y 2 on the left hand side is, in algebra, a circle.
The 8 on the right hand side is its maximum radius.
This maximum is varied by the expression x 2 + xy + y 2 , this being
the algebraic form of an ellipse.
The sine function keeps the overall effect circular.
The equation of this second example ArtGraph is
asn ( cos ( rnd ( 2 ) + y ) ) = acs ( sin ( rnd ( 2 ) + x ) )
It's more sophisticated in that it uses the sine, cosine, arc-sine
and arc-cosine functions along with some random integers.
Even so, it's well within what ArtGraph can handle.
As the arc-sine and arc-cosine functions are only defined upon
numbers between -1 and +1 their use is often immediately
followed by either sine or cosine.
Thus the equation above is less jumbled than it might at first appear.
This final example has equation
y * rnd ( int ( 6 ) ) - abs ( x ) * y = 5 sin ( y )
It again shows how a modest equation can give dramatic results,
this time by means of the integer and absolute value functions.
The sine function is giving the wave, and the 6 the six wave pairs
either side of the central y-axis.
Martin H Hansen, Shrewsbury School, Shrewsbury. SY3 7BA
All images, text and file downloads ( c ) 2006 & 2007, The MathMagical Software Company.