Dec 202017

The “Chaos Game”. Graphic demonstration that there really is order underlying “randomness”. Requires VGA and 286 or better. Includes C source. | |||
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File Name | File Size | Zip Size | Zip Type |

SIER.C | 2674 | 960 | deflated |

SIER.DOC | 2237 | 910 | deflated |

SIER.EXE | 50614 | 29117 | deflated |

SIER_1.C | 2887 | 1018 | deflated |

# Download File SIER.ZIP Here

## Contents of the SIER.DOC file

THE CHAOS GAME

One of the discoveries of the new science of Chaos is that there seems to be

an underlying order in randomness. Applying the simple rule of plotting a

point from a starting position - halfway to a randomly chosen vertex of an

arbitrary triangle, using the new point as the next beginning, and repeating

produces a strikingly orderly pattern. This so-called Sierpinsky Gasket

is a figure with a dimension of less than two, a fractal dimension.

Type SIER and see the triangle drawn, the "seed" point circled. This point

may be inside or outside the triangle, it matters not. Watch as the pattern

becomes illuminated in different colors showing which of the vertices has

been selected for any given plotted point.

The source code in the file SIER.C is made available for C programmers who

wish to do their own tinkering with the patterns. The file SIER_1.C is

source code for those wishing to try a variation, using an extra

"attractor" inside the triangle. The resulting pattern at first appears

more chaotic, but soon resolves itself into a visually interesting orderly

pattern.

============================================================================

1

*

START chosen at random * *

within or outside the triangle. * *

* *

* *

2nd point halfway to * o *

(randomly chosen) vertex * 2nd *

#1. * *

* *

* o o *

3rd point halfway to * START 3rd *

(randomly chosen) * *

vertex #3. 2 ************************** 3

Repeat thousands of times.

=============================================================================

SIER.EXE requires VGA graphics and a 286 or better machine to run.

It is Freeware, and the source code is herewith placed in the Public Domain.

M\Cooper

3138 Foster Ave.

Baltimore, MD 21224

One of the discoveries of the new science of Chaos is that there seems to be

an underlying order in randomness. Applying the simple rule of plotting a

point from a starting position - halfway to a randomly chosen vertex of an

arbitrary triangle, using the new point as the next beginning, and repeating

produces a strikingly orderly pattern. This so-called Sierpinsky Gasket

is a figure with a dimension of less than two, a fractal dimension.

Type SIER and see the triangle drawn, the "seed" point circled. This point

may be inside or outside the triangle, it matters not. Watch as the pattern

becomes illuminated in different colors showing which of the vertices has

been selected for any given plotted point.

The source code in the file SIER.C is made available for C programmers who

wish to do their own tinkering with the patterns. The file SIER_1.C is

source code for those wishing to try a variation, using an extra

"attractor" inside the triangle. The resulting pattern at first appears

more chaotic, but soon resolves itself into a visually interesting orderly

pattern.

============================================================================

1

*

START chosen at random * *

within or outside the triangle. * *

* *

* *

2nd point halfway to * o *

(randomly chosen) vertex * 2nd *

#1. * *

* *

* o o *

3rd point halfway to * START 3rd *

(randomly chosen) * *

vertex #3. 2 ************************** 3

Repeat thousands of times.

=============================================================================

SIER.EXE requires VGA graphics and a 286 or better machine to run.

It is Freeware, and the source code is herewith placed in the Public Domain.

M\Cooper

3138 Foster Ave.

Baltimore, MD 21224

December 20, 2017
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