.TH BIFUR1D 1
.SH NAME
.PD 0
.TP
bifur1d \- plot bifurcations from a one\-dimensional map
.PD 1
.SH SYNOPSIS
.PD 0
.TP
.B bifur1d \fB-help
.LP
\ \ or
.TP
.B bifur1d
\fB[\-width \fIinteger\fP]
[\-height \fIinteger\fP]
[\-skip \fIinteger\fP]
[\-rmin \fIdouble\fP]
[\-rmax \fIdouble\fP]
[\-func \fIstring\fP]
[\-factor \fIdouble\fP]
[\-ymin \fIdouble\fP]
[\-ymax \fIdouble\fP]
[\-aux \fIdouble\fP]
[\-box \fIinteger\fP]
[\-brmin \fIdouble\fP]
[\-brmax \fIdouble\fP]
[\-bymin \fIdouble\fP]
[\-bymax \fIdouble\fP]
[\-inv]
[\-mag \fIinteger\fP]
[\-term \fIstring\fP]
.PD 1
.SH DESCRIPTION
A bifurcation diagram is plotted for a one-dimensional map
according to the specified options. In general, the map is iterated
for several different values of the 'r' parameter so that the long
term behavior of the map can be observed as a function of
'r'. See the MAPS section of the manual page for details of what maps
are supported. User defined maps can be added to the file maps1d.c,
but you must recompile the program.
.SH OPTIONS
.IP \fB\-width\ \fIinteger\fP
Width of the plot in pixels.
.IP \fB\-height\ \fIinteger\fP
Height of the plot in pixels.
.IP \fB\-skip\ \fIinteger\fP
Number of initial points to skip.
.IP \fB\-rmin\ \fIdouble\fP
Smallest value for r.
.IP \fB\-rmax\ \fIdouble\fP
Largest value for r.
.IP \fB\-func\ \fIstring\fP
Map function to use (one of 'log', 'tent', 'sin', or 'gauss').
.IP \fB\-factor\ \fIdouble\fP
Multiplicative factor for number of iterates.
.IP \fB\-ymin\ \fIdouble\fP
Smallest value for y range.
.IP \fB\-ymax\ \fIdouble\fP
Largest value for y range.
.IP \fB\-aux\ \fIdouble\fP
Auxiliary map parameter.
.IP \fB\-box\ \fIinteger\fP
Line width for a box.
.IP \fB\-brmin\ \fIdouble\fP
Smallest r-value for the box.
.IP \fB\-brmax\ \fIdouble\fP
Largest r-value for the box.
.IP \fB\-bymin\ \fIdouble\fP
Smallest value for box y range.
.IP \fB\-bymax\ \fIdouble\fP
Largest value for box y range.
.IP \fB\-inv
Invert all colors?
.IP \fB\-mag\ \fIinteger\fP
Magnification factor.
.IP \fB\-term\ \fIstring\fP
How to plot points.
.SH MAPS
The following four one-dimensional maps are allowed:
.IP Logistic\ Map:
x(t+1) = 4 * r * x(t) * (1.0 - x(t))
.IP Tent\ Map:
x(t+1) = (x(t) <= 0.5) ? 2 * r * x(t) : 2r * (1.0 - x(t))
.IP Sine\ Map:
x(t+1) = sin(x(t) * PI * aux * 2 * r) / 2 + 0.5
.IP Gaussian\ Map:
x(t+1) = r * exp(-aux * (x(t) - 0.5) * (x(t) - 0.5))
.LP
See the file "maps1d.c" to see how to add user-defined maps.
.SH BUGS
No sanity checks are performed to make sure that any of the
options make sense.
.SH AUTHOR
Copyright (c) 1997, Gary William Flake.
Permission granted for any use according to the standard GNU
``copyleft'' agreement provided that the author's comments are
neither modified nor removed. No warranty is given or implied.