HIJ FONG !

Background: Chaos Mathematics

This game is based on chaos mathematics. Back in the 1970/80's a computer scientist/mathematician Benoit Mandelbrot discovered some maths functions that behaved in very strange ways. Instead of smoothly changing they became chaotic and unpredictable.

This fascinated the IBM scientist (who incidentally, was also paid by his employer to go up in planes and observe another chaotic phenomenon, the random shapes of clouds).

Natural Chaos: Nature will find a way

The film Jurrassic park features a chaos mathematician brought in to look at the park and decide whether it was safe or not. He concluded it was not. Nature would find a way to adapt, and what they had done at the park was introduce a life form. Life forms can adapt and change. He reasoned that the dinosaurs in the park, would adapt, and later escape from the island causing a disaster! As we know from the film, this did not take long!

Another example of chaos in nature was the spraying of crops by DDT in the 1950's and 60's. At first all the insects died off and the farmers had far better crop yields (but also poisoned all the fish in the rivers and killed many wild birds). But, a tiny proportion of the insects, through the natural chaos of DNA mutation, because resistant. This tiny proportion that could cope with DDT, having no competition with other insects, grew in population rapidly and after a few years caused worse crop yields than before DDT was introduced. Anyone interested in this should read "Silent Spring" by "Rachel Carson" written in 1962.

How to play

The program featured here starts with a blank tk graphics window. By clicking the mouse the chaotic function is revealed. Where in a stable zone the pixel is black. In a very chaotic zone the pixel is white. In a zone near the stable zone the pixel will be grey. Very near the ragged edge of the stable zone pixels will be coloured. The aim of the game is to find a pixel in the middle of the chaotic and the stable zone. Once this is clicked on the entire shape, previously hidden, is drawn in full on the screen.

Enjoy the chaos!

For Maths people

This game secretly rotates and resizes the hidden Mandelbrot shape. It does this using complex numbers which naturally have an angle of rotation and a sizing factor associated with them. Complex numbers are a pair of numbers, one real, the type of number we use every day, and a stranger one, an imaginary one. The imaginary numbers when multiplied become real numbers but minus! Most maths people use the term 'i' to denote a number if imaginary, but people who live in the real world, like electronic engineers (and python programmers) use 'j'. In fact, most 3D games now use a 4 dimiensional version of complex numbers called quaternions to rotate objects in the computer for you to shoot at!

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