Numerical performance

Curves do not need much calculations and are easy to generate. Rosettes, friezes and kaleidoscopes are different. They need many calculations for each pixel, often using several evaluations of trigonometric functions and exponential functions. Fortunately, our PCs are fast. A simple timing experiment shows that they can do approximately 10 million evaluations of the sine function per second. Is this fast enough ?

Not really, depending on the results you want. Typical low resolution images for the web have 512*512 pixels and thus a quarter of a million pixels. They need some tenths of a second to generate and that is tolerable. But if you want high-resolution images similar to digital cameras, then you will get around ten million pixels. This would make you wait for tens of seconds. Sure, that’s boring and we want to do better.

We can use tables to make much faster approximations of functions, as I will discuss in forthcoming posts. And we will see that there is a large difference in the speed of different browsers. This is important too for other image creation methods such as generative design and evolutionary creation.

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