# First year inspired pictures

This is just a very small number of pictures inspired by tutoring
first year maths at Warwick University.

Click on the links (green) to go to interative versions of these programs,
mostly controlled by mouse movement. These work on Safari and Chrome, and
are written in JavaScript/Webgl

## Osculating circles

The first file has some detailed explanation of a simple example of
how to draw osculating circles for a sin curve. The other examples
are doodles based on this, where the curve varies, more than one
osculating circle is drawn, or the circle only have a central part drawn,
but from where the center should be.
## Change of Basis

## Level sets and gradient

The first of these shows the level sets and gradient for
a quadratic function. Then there are versions with different functions
(Perlin noise), and the fact this is a picture of level sets and gradients
is more hidden. In the first picture, the colouring and shading is according\
to level sets, and the arrows are determined by the gradient function.
This is true for the other pictures too, but I have left out the arrowheads,
drawn the lines longer so they meet up,
and coloured the level sets black periodically to give the impression of
bands, which can be modified to look like they are woven, just depending on
whether the level set or the gradient lines are drawn first.

So there is a kind of blur between maths and art - I would call this mathematical doodling.