Last Update Apr. 8, 2000  日本語はこちら


    Checking the equation expressing the phenomenon of biological proliferation with the perfect alternation of generation "Xn+1 = A Xn ( 1 - Xn )" we can see as follows;
      1<a<=2 : coverge to 1-1/A
      2<a<=3 : oscillating approach to a limit value 1-1/A
      3<a<=4 : fall into an oscillation or into Chaos

    To confirm this I put the result value along Y axis with "n=75-100" along Z axis and with "A=0.9-4.0" along X axis.

    Scene file : lpchjunc.txt

Junction / 55k / Apr. 2000 / by Tsutomu Higo

    I modified a famous Chaos equation Henon. This equation is known as 2 dimensional figue. I forced this to 3 dimensional figue by Z=X*Y.

    Scene file : lpchenon.txt

Henon / 79k / Apr. 2000 / by Tsutomu Higo

    So many patterns appear one after another with the modifying coefficient.
    It may be joyful to see details of some from them. Or it may be interesting to serch new patterns behind them by more fine modification.

    Scene file : lpchvary.txt

Variety / 48k / Apr. 2000 / by Tsutomu Higo

    Like a Persian rug the pattern extends with increasing "n". It is marvelously complicated.

    Scene file : lpchrug.txt

Rug / 90k / Apr. 2000 / by Tsutomu Higo

    I put side by side the XY plane spheres along Z axis with modifying coefficient to see the pattern modification.
    How about this? I've confused slightly with this.

    Scene file : lpchwind.txt

Winding / 88k / Apr. 2000 / by Tsutomu Higo

    I made this image by the way of upper "Winding". I used large "n" number on only the part like flower pedals. In a sense this image is a combination of a plane and a solid.
    This image may be perfect if there is a princess with long hair.

    Scene file : lpchtowr.txt

Tower / 65k / Apr. 2000 / by Tsutomu Higo

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