The PAL frame rate 25 frames per second and NTSC frame rate are derived from frequency and interlacing.
Incidently the PAL /NTSC are colour systems and don't really have anything to do with framerate but just happen to be mostly used in the countries that use a specific framerate although there are exceptions.

In order to work TV receivers require a source of field timing reference signals. These are signals that tell the TV receiver to be ready to receive the next picture in the stream of images. Early set designers decided to use the Mains power supply frequency as this source for two good reasons. The first was that with the older types of power supply, you would get rolling hum bars on the TV picture if the mains supply and power source were not at exactly the same frequency. The second was that the TV studios would have had enormous problems with flicker on their cameras when making programmes.

All movies that are made for Cinema are shot at 24 frames per second but to show them on TV you have to have two interlaced pictures scanned alternately across the screen and since the European frequency is 50Hz you have two lots of 25 frames per second,while in the States and Asia the frequency is 60Hz hence you get 30 frames per second (the fieldrate was later changed to 59.94Hz when colour was introduced)hence the true frame rate is 29.97fps.
The odd number you are quoting 23.76 is the result from converting a 30 fps movie made for tv to a 24fps so it can be shown on a PAL system (it's played at 25fps but you don't really notice it's running fast ) or Movie Theater and it's achieved by actually removing frames in a given sequence through out the movie ,sometimes called 3/2 pulldown it's not an ideal framerate but it works to get the movie to play.


Sorry for highjacking the thread but i felt that since this topic was mentioned then the info should be clarified.

Weyu
A nice start but as others have mentioned the butterfly movement needs some work.