This is some art work based on osculating circles of the sin graph.
I first wrote the first slide of this to illustrate osculating circles in a tutorial when
first year were covering the concept of osculating circles, but I thought it would be fun
to base some art work round the concept. I talked about this at the 25th Generative art conference
in Rome, December 2022; I've slightly modified the slides since then. The original slides are
, and in particular I also talked a bit about art work produced
corresponding to talking about gradient in tutorials.
In these pictures, parameters are determined by a dot, which you can move by the dot. The dot
will be moved by the mouse as long as the mouse is not in the area at the top of the screen.
The dot stops moving if you click. This is only programmed to work with a mouse, not touch screen,
and was written using a macbook pro. If you click the screen to stop the mouse, then you can use
the slider to show the configuration in different styles. A few of the slides towards the end do
not depend on the dot.
The sin(x) button can be clicked to show an indication of the sin curve underlying the
circles picture. The dot button can be used to hide the control dot.
The first slide shows one point on the curve, and its corresponding osculating circle.
Most of the rest of the slides show several circles, usually around 20. These are osculating circles
points on graph, starting with the point corresponding to the dot, and with
the with the distances
between x values of successive points determined by the y coordinate of the dot, so the points
for which osculating circles are drawn will be closer or further apart.