The Circle Map Room

The Circle Map Room contains pictures of various portions of the Hausdorf Measure of the iterated Forced Osccilator (Circle Map) Equation. Dark areas, known as Arnold's Tongues, represent regions of mode-locked (phase-locked) behaviour.

iterated eqn. view of the central region of the Hausdorff measure of the iterated Circle Map (Dark areas are Arnold's Tongues).

iterated eqn. Same as above, but with different color scheme, in an attempt to highlight certain details.

iterated eqn. A close-up of the central region of the picture above.

iterated eqn. As above, but differnt view.

The Center of the Circle

The circle posseses many mysteries, and has been a focus for man's attentions before language. Drawn in the sand, it is a symbol for for all around. The sun, the moon. Later, the wheel, the coin. During the renaissance, Galileo and the Church feuded over "epicycles", the circles-within-circles that were the law of the heavens, and ruled over planetary motions. The same era began the first studies of the "simple harmonic oscillator", that is, the study of circular motions and vibrations (harmony). In the previous era, man discovered that all things electrical are ruled by these theories of circular harmony. In our era, Quantum Mechanics has raised the harmonic oscillator to the highest alter: that of zero-point motion. While it is said that the theories of chaos will soon wreck the dominance of the theories of the circle, this is simply not true. The circle will previal, for the very mysteries of chaos itself can be found within its center.

The files circle.gif, red_circle.gif, flame.gif and earth.gif all show pictures of the center of the circle. More spcifically, we see the Huasdorff measure of the iterated Circle Map (the horced harmonic oscillator), showing the contorted, forking Arnold's tongues.

circle.gif -- the center of the circle.

red_circle.gif -- the same, but in red.

flame.gif -- the fire in the center of the circle.

earth.gif -- the scary, dark shadow under the flame, arms outstreached, seeking to embrace.

Copyright (c) 1991, 1994 Linas Vepstas All rights reserved.

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The Circle Map Room by Linas Vepstas is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.