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1995-07-25
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LLLLDDDDSSSS((((6666XXXX)))) UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVV LLLLDDDDSSSS((((6666XXXX))))
NNNNAAAAMMMMEEEE
lds - generate and display a lattice dynamical system
SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
_l_d_s [-2APcdmpq] [-W _w_i_d_t_h] [-H _h_e_i_g_h_t] [-w _w_i_d_e] [-h _h_i_g_h]
[-i _i_n_i_t] [-n _l_a_m_b_d_a ] [-b _n ] [-F _f_r_e_q] [-B _f | _r | _n ]
[-C _e_p_s_i_l_o_n_1 ] [-L _e_p_s_i_l_o_n_2 ] [-R _e_p_s_i_l_o_n_3 ] [-r _d_e_l_t_a ]
[-E _r_h_o ] [-M _o_m_e_g_a ] [-T _h_e_i_g_h_t] [-o _f_n_a_m_e]
DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
_l_d_s generates and displays a sequence of curves or cellular
automata like figures which graphically represent the
evolution of a Lattice Dynamical System (LDS). An LDS is an
array of cells, each of which represents a dynamical system.
Each cell is coupled to its nearest neighbors. The dynamical
systems available in this software package are currently the
logistic map, circle map and tent map. The state of each
cell in the LDS is a real number in the unit interval. The
evolution of the lattice is determined by an iteration thru
the specified dynamic (e.g. the logistic equation) followed
by a weighted averaging with its nearest neighbors.
By default, _l_d_s calculates and displays a 1-dimensional LDS.
A 2-dimensional LDS can be specified on the command line
(see the descriptions of the -_h, -_2 and -_H options below).
In the 2-D case, nearest neighbors are defined to be left,
right, upper and lower (no diagonal neighbors). In the 1-D
case, nearest neighbors are simply left and right.
Command line arguments and run-time keyboard input allow lds
to simulate a wide variety of lattice dynamical systems. The
user can specify the dynamic to be used, the non-linearity
parameter, the strength of coupling, the initial conditions,
the size of the array, the lenght of the run, whether and
how to evolve connection strengths, and more. During the
run, the display of an evolving 1-D LDS can either be CA-
like with each generation being represented as a horizontal
line evolving upward in the window or as points or a curve
with X axis the lattice and Y-axis the cell states [0,1].
The display of an evolving 2-D LDS can either be CA-like
with each generation being represented as a rectangle
evolving upward in the window or as points or a curve with X
axis the projected lattice and Y-axis the cell states [0,1].
In addition, graphical display of cell states can be toggled
between actual state and phase difference with left
neighbor.
Site and spatial histogram windows can also be displayed.
The X-axis for the site histogram curve is the unit interval
[0,1] while the Y-axis is the number of lattice sites which
Page 1 (printed 7/3/94)
LLLLDDDDSSSS((((6666XXXX)))) UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVV LLLLDDDDSSSS((((6666XXXX))))
have taken on that value. The X-axis for the spatial
histogram window is the projection of the lattice down onto
its horizontal width while the Y-axis is the unit interval
[0,1].
Lattice dynamical systems are also referred to as coupled
map lattices.
OOOOPPPPTTTTIIIIOOOONNNNSSSS
----2222
Default to a two dimensional lattice. Defaults for width
and height are now 256x256.
----AAAA
Creates site histogram curve
----pppp
Indicates draw phase 1st differences
----qqqq
Indicates not to draw "quilt" style. In quilt mode, the
lattice is moved upward in the window each generation (if
the window is larger than the lattice). If the "-q" option
is specified, subseqeunt generations overwrite the previous
one.
----cccc
Indicates draw curves
----PPPP
Indicates draw points (when in curve drawing mode)
----mmmm
Indicates monochrome plot
----BBBB [[[[ ffff |||| rrrr |||| _b]
Selects fixed zero, random, or specified fixed value of
boundaries. Option -Bf sets boundaries to zero; -Br
selects randomly fluctuating boundaries; and -Bb assigns
value 0 < b < 1 to boundaries. The default boundary
specification is periodic.
----wwww _n
Indicates the lattice is _n cells wide (default is full
screen)
----hhhh _n
Indicates the lattice is _n cells high (default is 1 in
the absense of the -_2 argument and 256 when -_2 is specified)
----WWWW _n
Indicates the windows are _n pixels wide (default is full
screen)
----HHHH _n
Indicates the windows are _n pixels high (default is full
screen in the absense of the -_2 argument and 256 when -_2 is
specified)
----iiii [[[[ pppp _n | _n_n_n_n | r ]
Selects initial condition. Option -ip _n indicates
periodic initial conditions with frequency _n. Option -i
_n_n_n_n_n indicates center cells are given values _1/_n.
Page 2 (printed 7/3/94)
LLLLDDDDSSSS((((6666XXXX)))) UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVV LLLLDDDDSSSS((((6666XXXX))))
Option -ir selects random initial conditions (which is
the default)
----nnnn [[[[ rrrr |||| llll |||| pppp _m | lambda ]
Selects non-linearity parameter values (default is 3.7).
Option -nr selects randomly assigned non-linearity
parameters. Option -nl selects linearly assigned non-
linearity parameters. Option -np _m selects periodically
assigned non-linearity parameters with frequency _m.
Option -n lambda selects non-linearity parameter lambda
for all sites.
----bbbb _n
Begin graphing at generation _n (default is 1)
----FFFF _n
Indicates display every _n'_t_h generation (1 is default)
----CCCC _e_p_s_i_l_o_n_1
Indicates weight of center cell (default 0.9) where 0 <
epsilon1 < 1.
----LLLL _e_p_s_i_l_o_n_2
Indicates weight of left neighbor (default 0.05) where 0
< epsilon2 < 1.
----RRRR _e_p_s_i_l_o_n_3
Indicates weight of right neighbor (default 0.05) where 0
< epsilon3 < 1.
----rrrr _d_e_l_t_a
Indicates range outside of which differences are graphed
(0 < delta < 1) This value also serves as the determining
distance over which connection strengths weaken rather
than strengthen (when the -E flag is specified).
----EEEE _r_h_o
Indicates the rate at which connection strengths evolve
(0 < rho < 1). Connection strengths do not change if no
-E flag is present.
----MMMM _o_m_e_g_a
Selects circle map
----TTTT _h_e_i_g_h_t
Selects tent map
----oooo _f_n_a_m_e
Outputs graphed generations to file _f_n_a_m_e.
NNNNOOOOTTTTEEEESSSS
In the absence of either the -M or -T arguments, the
logistic map is used.
During display, use of the keys _1_2_3_4_5_6_7_8_9+-
<>_B_D_E_F_H_I_L_P_Q_R_S_W_X_c_d_f_h_i_m_p_s_w_x_q? indicates:
(_1-_9) _S_e_t _t_h_e _f_r_e_q_u_e_n_c_y _t_o _1-_9
(+) _I_n_c_r_e_m_e_n_t _t_h_e _f_r_e_q_u_e_n_c_y _b_y _1
(-) _D_e_c_r_e_m_e_n_t _t_h_e _f_r_e_q_u_e_n_c_y _b_y _1
(>) _D_o_u_b_l_e _t_h_e _f_r_e_q_u_e_n_c_y
(<) _H_a_l_v_e _t_h_e _f_r_e_q_u_e_n_c_y
Page 3 (printed 7/3/94)
LLLLDDDDSSSS((((6666XXXX)))) UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVV LLLLDDDDSSSS((((6666XXXX))))
_(_B_) _B_e_g_i_n _a_g_a_i_n
_(_c_) _t_o_g_g_l_e _c_u_r_v_e_/_c_e_l_l _d_i_s_p_l_a_y
_(_d_) _d_r_a_w
_(_D_) _F_l_u_s_h _t_h_e _d_r_a_w_i_n_g _b_u_f_f_e_r
_(_E_) _E_r_a_s_e _e_a_c_h _g_e_n_e_r_a_t_i_o_n
_(_f _o_r _F_) _S_a_v_e _t_h_e _d_r_a_w_i_n_g _w_i_n_d_o_w _t_o _a _f_i_l_e
_(_h_) _D_i_s_p_l_a_y _h_i_s_t_o_g_r_a_m _c_u_r_v_e
_(_H_) _H_i_s_t_o_g_r_a_m _t_r_a_c_k_i_n_g _t_o_g_g_l_e_d
_(_I_) _I_n_c_r_e_m_e_n_t _t_h_e _s_t_r_i_p_e _i_n_t_e_r_v_a_l
_(_i_) _D_e_c_r_e_m_e_n_t _t_h_e _s_t_r_i_p_e _i_n_t_e_r_v_a_l
_(_L_) _L_i_n_e_s _d_r_a_w_n
_(_m_) _m_u_l_t_i_-_s_t_e_p
_(_p_) _T_o_g_g_l_e _d_i_s_p_l_a_y _o_f _p_h_a_s_e _1_s_t _d_i_f_f_e_r_e_n_c_e_s
_(_P_) _P_o_i_n_t_s _d_r_a_w_n
_(_R_) _S_p_i_n _t_h_e _c_o_l_o_r _w_h_e_e_l
_(_s_) _s_i_n_g_l_e _s_t_e_p
_(_S_) _S_p_i_n _t_h_e _c_o_l_o_r _w_h_e_e_l _a_n_d _i_n_c_r_e_m_e_n_t _t_h_e _s_p_i_n _l_e_n_g_t_h
_(_w_) _D_e_c_r_e_m_e_n_t _t_h_e _c_o_l_o_r _w_h_e_e_l _i_n_d_e_x
_(_W_) _I_n_c_r_e_m_e_n_t _t_h_e _c_o_l_o_r _w_h_e_e_l _i_n_d_e_x
_(_x_) _C_l_e_a_r _t_h_e _w_i_n_d_o_w
_(_X_) _T_o_g_g_l_e _c_o_m_p_l_e_x _d_y_n_a_m_i_c_a_l _s_y_s_t_e_m_s _m_o_d_e
_(_Q _o_r _q_) _q_u_i_t
AAAAUUUUTTTTHHHHOOOORRRR
_l_d_s was written by Ronald Record. Questions, suggestions,
and comments may be directed via e-mail to rr@sco.com or
...uunet!sco!rr.
RRRREEEEFFFFEEEERRRREEEENNNNCCCCEEEESSSS
The literature is sparse but includes the following
excellent papers :
"Lyapunov Analysis and Information Flow in Coupled Map
Lattices" by Kunihiko Kaneko, Physica 23D (1986) 436-447
"Spatiotemporal Chaos in One- and Two- Dimensional Coupled
Map Lattices" by Kaneko
"Spatiotemporal Chaos and Noise" by Gottfried Mayer-Kress
and Kaneko, J. Stat. Phys.(1988)
"Pattern Competition Intermittency and Selective Flicker
Noise in Spatiotemporal Chaos" by Kaneko, Physics Letters A,
V125, 1 (1987)
"Pattern Dynamics in Spatiotemporal Chaos" by Kaneko (1987)
"Phenomenology of Spatial-Temporal Chaos" by Jim Crutchfield
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LLLLDDDDSSSS((((6666XXXX)))) UUUUNNNNIIIIXXXX SSSSyyyysssstttteeeemmmm VVVV LLLLDDDDSSSS((((6666XXXX))))
and Kaneko, appearing as a chapter in "Directions in Chaos"
edited by Hao Bai-lin, World Scientific Publishing (1987)
"Robust Space-Time Intermittency and 1/f Noise" by James
Keeler and Doyne Farmer, Physica 23D (1986) 413-435
Page 5 (printed 7/3/94)