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       epicycle - draws a point moving around a circle which moves around a cicle which...

       epicycle  [-display host:display.screen] [-root] [-window] [-mono] [-install] [-noinstall]
       [-visual viz] [-colors  N]  [-foreground  name]	[-color-shift  N]  [-delay  microseconds]
       [-holdtime  seconds]  [-linewidth N] [-min_circles N] [-max_circles N] [-min_speed number]
       [-max_speed number]  [-harmonics  N]  [-timestep  number]  [-divisor_poisson  probability]
       [-size_factor_min number] [-size_factor_max number]

       The  epicycle  program draws the path traced out by a point on the edge of a circle.  That
       circle rotates around a point on the rim of another circle, and so on, several times.  The
       random  curves  produced  can be simple or complex, convex or concave, but they are always
       closed curves (they never go in indefinitely).

       You can configure both the way the curves are drawn  and  the  way  in  which  the  random
       sequence of circles is generated, either with command-line options or X resources.

       -display host:display.screen
	       Specifies which X display we should use (see the section DISPLAY NAMES in X(1) for
	       more information about this option).

       -root   Draw on the root window.

       -window Draw on a newly-created window.	This is the default.

       -mono   If on a color display, pretend we're on a monochrome display.  If we're on a  mono
	       display, we have no choice.

	       Install a private colormap for the window.

	       Don't install a private colormap for the window.

       -visual viz
	       Specify	which visual to use.  Legal values are the name of a visual class, or the
	       id number (decimal or hex) of a specific visual.  Possible choices include

	       default, best, mono, monochrome, gray, grey, color, staticgray, staticcolor, true-
	       color, grayscale, greyscale, pseudocolor, directcolor, number

	       If  a  decimal  or  hexadecimal number is used, XGetVisualInfo(3X) is consulted to
	       obtain the required visual.

       -colors N
	       How many colors should be used (if possible).  The colors are chosen randomly.

       -foreground name
	       With -mono, this option selects the foreground colour.

       -delay microseconds
	       Specifies the delay between drawing successive line segments of the path.   If you
	       do  not	specify  -sync,  some  X  servers may batch up several drawing operations
	       together, producing a less smooth effect.   This is more likely to happen in mono-
	       chrome mode (on monochrome servers or when -mono is specified).

       -holdtime seconds
	       When the figure is complete, epicycle pauses this number of seconds.

       -linewidth N
	       Width  in  pixels  of  the  body's track.   Specifying values greater than one may
	       cause slower drawing.   The fastest value is usually zero, meaning one pixel.

       -min_circles N
	       Smallest number of epicycles in the figure.

       -max_circles N
	       Largest number of epicycles in the figure.

       -min_speed number
	       Smallest possible value for the base speed of revolution of  the  epicycles.   The
	       actual speeds of the epicycles vary from this down to min_speed / harmonics.

       -max_speed number
	       Smallest possible value for the base speed of revolution of the epicycles.

       -harmonics N
	       Number  of  possible harmonics; the larger this value is, the greater the possible
	       variety of possible speeds of epicycle.

       -timestep number
	       Decreasing this value will reduce the distance the body moves for each  line  seg-
	       ment,  possibly	producing  a  smoother	figure.  Increasing it may produce faster

       -divisor_poisson probability
	       Each epicycle rotates at a rate which is a factor of the base speed.  The speed of
	       each epicycle is the base speed divided by some integer between 1 and the value of
	       the -harmonics option.  This integer is decided by starting at  1  and  tossing	a
	       biased  coin.   For  each  consecutive head, the value is incremented by one.  The
	       integer will not be incremented above the value of  the	-harmonics  option.   The
	       argument  of  this option decides the bias of the coin; it is the probability that
	       that coin will produce a head at any given toss.

       -size_factor_min number
	       Epicycles are always at least this factor smaller than their parents.

       -size_factor_max number
	       Epicycles are never more than this factor smaller than their parents.

       Option		 Resource		Default Value
       ------		 --------		-------------
       -colors		 .colors		100
       -delay		 .delay 		1000
       -holdtime	 .holdtime		2
       -linewidth	 .lineWidth		4
       -min_circles	 .minCircles		2
       -max_circles	 .maxCircles		10
       -min_speed	 .minSpeed		0.003
       -max_speed	 .maxSpeed		0.005
       -harmonics	 .harmonics		8
       -timestep	 .timestep		1.0
       -divisor_poisson  .divisorPoisson	0.4
       -size_factor_min  .sizeFactorMin 	1.05
       -size_factor_max  .sizeFactorMax 	2.05
			 .timestepCoarseFactor	1.0
       Before the drawing of the figure is begun, a preliminary calculation of the path  is  done
       in order to scale the radii of the epicycles so as to fit the figure on the screen or win-
       dow.  For the sake of speed, This calculation is done with  a  larger  timestep	than  the
       actual drawing.	The time-step used is the value of the -timestep option multiplied by the
       timestepCoarseFactor resource.  The default value of 1 will almost always work fast enough
       and so this resource is not available as a command-line option.

       The  program  runs  mostly  without user interaction.  When running on the root window, no
       input is accepted.  When running in its own window, the program will exit if mouse  button
       3  is pressed.  If any other mouse button is pressed, the current figure will be abandoned
       and another will be started.

       The geometry of epicycles was perfected by Hipparchus of Rhodes at some	time  around  125
       B.C.,  185 years after the birth of Aristarchus of Samos, the inventor of the heliocentric
       universe model.	Hipparchus applied epicycles to the Sun and the Moon.  Ptolemy of Alexan-
       dria went on to apply them to what was then the known universe, at around 150 A.D.  Coper-
       nicus went on to apply them to the heliocentric model at the beginning  of  the	sixteenth
       century.   Johannes  Kepler discovered that the planets actually move in elliptical orbits
       in about 1602.  The inverse-square law of gravity  was  suggested  by  Boulliau	in  1645.
       Isaac  Newton's Principia Mathematica was published in 1687, and proved that Kepler's laws
       derived from Newtonian gravitation.

       The colour selection is re-done for every figure.  This	may  generate  too  much  network
       traffic for this program to work well over slow or long links.

       Copyright (C) 1998, James Youngman.  Permission to use, copy, modify, distribute, and sell
       this software and its documentation for any purpose is hereby granted  without  fee,  pro-
       vided  that  the  above copyright notice appear in all copies and that both that copyright
       notice and this permission notice appear in supporting documentation.  No  representations
       are  made  about the suitability of this software for any purpose.  It is provided "as is"
       without express or implied warranty.

       James Youngman <jay@gnu.org>, April 1998.

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