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.
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
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 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 segment, possibly producing 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.
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 heliocentric 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 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.
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.
