68 lines
2.9 KiB
Markdown
68 lines
2.9 KiB
Markdown
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HIJ FONG !
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Background: Chaos Mathematics
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-----------------------------
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This game is based on chaos mathematics.
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Back in the 1980's a computer scientist/mathematician
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Benort Mandelbrot discovered some maths functions that
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behaved in very stange ways. Instead of smoothly changing
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they became chaotic and unpredictable.
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This facinated the IBM scientist (who incidentally, was also paid by his employer to
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go up in planes and observe another chaotic phenomenem, the random shapes of clouds).
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Natural Chaos: Nature will find a way
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The film Jurasic park features a chaos mathmetician brought in to
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look at the park and decide whether it was safe or not.
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He conclusded it was not. Nature would find a way to adapt, and
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what they had done at the park was introduce a life form. Life forms can
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adapt and change. He reasoned that the dinosaurs in the park, would adapt, and
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later escape from the island causing a disaster!
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As we know from the film, this did not take long!
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Another example of chaos in nature was the spraying of crops by DDT
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in the 1950's and 60's. At first all the insects died off and the farmers
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had far better crop yields (but also poisoned all the fish in the rivers and killed many wild birds).
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But, a tiny proportion of the insects, through the natural chaos
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of DNA mutation, because resistant. This tiny proportion that could cope with DDT, having no competition
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with other insects,
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grew in population rapidly and after a few years caused worse crop yields than before DDT
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was introduced. Anyone interested in this should read "silent spring" by "rachel carson"
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written in 1962.
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How to play
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The program featured here starts with a blank tk graphics window. By clicking the mouse
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the chaotic function is revealed. Where in a stable zone the pixel is black.
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In a very chaotic zone the pixel is white. In a zone near the stable zone
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the pixel will be grey. Very near the ragged edge of the stable zone
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pixels will be coloured.
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The aim of the game is to find a pixel in the middle of the chaotic and
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the stable zone.
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Once this is clicked on the entire shape, previously hidden, is drawn in full on the screen.
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Enjoy the chaos!
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For Maths people
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----------------
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This game secretly rotates and resizes the hidden mandelbrot shape.
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It does this using complex numbers which naturally have an angle of rotation
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and a sizing factor associated with them.
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Complex numbers are a pair of numbers, one real, the type of number
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we use every day, and a stranger one, an imaginary one.
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The imaginary one when multiplied by itsself becaomes a real number but minus!
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Most maths people use the term 'i' to denote a number if imaginary,
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but people who live in the real world, like electronic engineers
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(and python programmers) use 'j'.
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In fact, most 3D games now used a 4 dimiensional version of complex numbers
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called quaternions to rotate objects in the computer for you to shoot at!
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