xscreensaver(1)

NAME

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

SYNOPSIS

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 proba_
bility] [-size_factor_min number]  [-size_factor_max  num_
ber]

DESCRIPTION

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 com
plex, 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 gener
ated, either with command-line options or X resources.

OPTIONS

-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

Install a private colormap for the window.

-noinstall

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, truecolor,
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
monochrome 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 rev
olution 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 rev
olution of the epicycles.

-harmonics N

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

-timestep number

Decreasing this value will reduce the distance the
body moves for each line segment, possibly produc
ing a smoother figure. Increasing it may produce
faster results.

-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.

RESOURCES

Array-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 window. 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.

USER INTERFACE

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.

HISTORY

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 helio
centric universe model. Hipparchus applied epicycles to
the Sun and the Moon. Ptolemy of Alexandria went on to
apply them to what was then the known universe, at around
150 A.D. Copernicus went on to apply them to the helio
centric 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 gravita
tion.

BUGS

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

Copyright © 1998, James Youngman. Permission to use,
copy, modify, distribute, and sell this software and its
documentation for any purpose is hereby granted without
fee, provided 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.

AUTHOR

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

X Version 11 27-Apr-97 XScreenSaver(1)