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+
+* HIJ FONG !
+
+** Background: Chaos Mathematics
+
+This game is based on chaos mathemeatics.
+Back in the 1980's a computer scientist/matmmmatician
+Benort Mandelbrot discovered some maths functions that
+behaved in very stange ways. Instead of smoothly changing
+they became chaotic and unpredictable.
+
+This facinated the IBM scientist (who incidentally, was also paid by his employer to
+go up in planes and observe another chaotic phenomenem, the random shapes of clouds).
+
+** Natural Chaos: Nature will find a way
+
+The film Jurasic park features a chaos mathmetician brought in to
+look at the park and decide whether it was safe or not.
+He conclusded 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
+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"
+writtin 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 one when multiplied by itsself becaomes a real number 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 used a 4 dimiensional version of complex numbers
+called quaternions to rotate objects in the computer for you to shoot at!
+