Hey all, and thanks for any help and feedback,
I will be doing a presentation soon in which I wanted to show the audience some maths they are unlikely to have come across at school. I thought that showing them the creation of a fractal would be good, as the idea behind making it can be simple and the end product be a very complex and pretty picture.
As they will not know about complex numbers, I don't want to do a Julia set or the Mandelbrot one. I thought that it'd be better to do a fractal based on a chaotic system. I have decided on the following:
A swinging pendulum suspended above three magnets, starting at various points and swinging as according to the forces from the three magnets, gravity, and a damping force proportional to the angular speed. The magnet which the pendulum ends up suspended above would define the colour of the starting position either red, green or blue (perhaps), maybe also the time taken to come to rest could help define the colour, to make the fractal more pretty.
I have arrived at a set of formula to describe the acceleration of the pendulum according to angular position, so all that would remain would be to create a computer program to do the calculations and create the picture.
So I write asking for advice as to whether there exists a program which I could use to do this. It would be good if it could allow me to write a program to process each pixel, then colour the pixel, producing an image in the end. I would prefer if it could do this while showing the picture on screen, as it is being created.
Also it would be good if I could use the program to display an animation of a point tracing out the curve of the pendulum, to show the audience what kind of motion the equations are modelling.
I am used to creating programs like this on my TI-82 (to draw the Mandelbrot set etc.), however this obviously cannot output in colour, it is pretty slow, and it is inconvenient to show to a large audience.
So any suggestions and pointers would be very much appreciated,