#### NAME

bifur1d - plot bifurcations from a one-dimensional map

#### SYNOPSIS

**bifur1d** **-help**
or
**bifur1d**
**[-width** *integer***]** **[-height** *integer***]** **[-skip** *integer***]**
**[-rmin** *double***]** **[-rmax** *double***]** **[-func** *string***]** **[-fac-**
**tor** *double***]** **[-ymin** *double***]** **[-ymax** *double***]** **[-aux**
*double***]** **[-box** *integer***]** **[-brmin** *double***]** **[-brmax** *dou-*
*ble***]** **[-bymin** *double***]** **[-bymax** *double***]** **[-inv]** **[-mag**
*integer***]** **[-term** *string***]**

#### 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' param-
eter so that the long term behavior of the map can be
observed as a function of are supported. User defined
maps can be added to the file maps1d.c, but you must
recompile the program.

#### OPTIONS

**-width** *integer*
Width of the plot in pixels.
**-height** *integer*
Height of the plot in pixels.
**-skip** *integer*
Number of initial points to skip.
**-rmin** *double*
Smallest value for r.
**-rmax** *double*
Largest value for r.
**-func** *string*
Map function to use (one of 'log', 'tent', 'sin',
or 'gauss').
**-factor** *double*
Multiplicative factor for number of iterates.
**-ymin** *double*
Smallest value for y range.
**-ymax** *double*
Largest value for y range.
**-aux** *double*
Auxiliary map parameter.
**-box** *integer*
Line width for a box.
**-brmin** *double*
Smallest r-value for the box.
**-brmax** *double*
Largest r-value for the box.
**-bymin** *double*
Smallest value for box y range.
**-bymax** *double*
Largest value for box y range.
**-inv** Invert all colors?
**-mag** *integer*
Magnification factor.
**-term** *string*
How to plot points.

#### MAPS

The following four one-dimensional maps are allowed:
Logistic Map:
x(t+1) = 4 * r * x(t) * (1.0 - x(t))
Tent Map:
x(t+1) = (x(t) <= 0.5) ? 2 * r * x(t) : 2r * (1.0 -
x(t))
Sine Map:
x(t+1) = sin(x(t) * PI * aux * 2 * r) / 2 + 0.5
Gaussian Map:
x(t+1) = r * exp(-aux * (x(t) - 0.5) * (x(t) -
0.5))
See the file "maps1d.c" to see how to add user-defined
maps.

#### BUGS

No sanity checks are performed to make sure that any of
the options make sense.

#### AUTHOR

Copyright (c) 1997, Gary William Flake.
Permission granted for any use according to the standard
GNU ``copyleft'' agreement provided that the author's com-
ments are neither modified nor removed. No warranty is
given or implied.