Delila Program: sphere

sphere program

Documentation for the sphere program is below, with links to related programs in the "see also" section.

{   version = 1.48; (* of sphere.p 2014 Dec 06}

(* begin module describe.sphere *)
   sphere: plot density of Shannon spheres

   sphere(spherep: in, sigma: out, xyin: out, output:out)

   spherep: parameters.
     The first line is the step size interval (0.01 works well).

     the second line is the maximum radius to calculate out to (= maxr,
         3.1 works well).

     Each following line is a dimension to plot.

     If the dimension number is negative, it must be followed on the same line
     by the coordinates of the position to place the dimension numeral.
     The absolute value of the dimension is used in the calculation.

     If the dimension is negative AND not an integer, the coordinates of the
     position must be followed by the number of decimal places to display
     the dimension.

   sigma: lists the estimates for Rmaximum +/- sigma,
      taken as the radius when the curve passes through exp(-1/2).

   xyin: input to xylop, the plot

   output: messages to the user

   Create a graph of radius versus density of Shannon spheres
   at various given dimensions.  The output is run through xyplo.

   The function is:

   pd(R) = R^(D-1) * exp(-R^2/(2* sigma^2))

   where '^' means to exponentiate and
   where sigma^2 * (D-1) - Rmaximum^2
   so setting Rmaximum = 1 relates sigma and D.

   The graph is in the range (0,0) to (r=maxr,1)).
   The curve is normalized so that its maximum is at (1,1).
   (except when dimension = 1, where it is at (1,0).

   Since xyplo can't plot several separate curves, without being
   told each symbol, this program simply starts at (0,pd(r)), draws
   the curve to (maxr,pd(maxr)), then circles back by drawing lines
   to the x axis (2*maxr,0) and then the origin (0,0).  By setting
   the region that xyplo plots below maxr, one gets nice, fully
   correct curves that do not appear to be connected.

   [1988 jan 23,5]

author = "T. D. Schneider",
title = "Theory of Molecular Machines.
{I. Channel} Capacity of Molecular Machines",
journal = "J. Theor. Biol.",
volume = "148",
thenumber = "1",
pages = "83-123",
comment = "{(Note: The figures were printed out of order!
Fig. 1 is on p. 97)}",
note = "\htmladdnormallink
year = 1991}

see also

   Schneider.ccmm paper:

   example parameters: spherep
   example plotting file for xyplo: sphere.xyplop
   plotting program: xyplo.p

   resulting graph, postscript ... :
   resulting graph, jpg .......... :
   image for sphereinteger

   example of fractal graph parameters: spherep.fractal
   resulting graph, postscript ... :
   resulting graph, jpg .......... :
   image for spherefractal

   Related programs:
   compress D dimensional sphere to 2D: ... ring.p
   plot output of ring: ................... riden.p
   Match fdr curve: ....................... fdr.p

   Thomas Dana Schneider

   none known

(* end module describe.sphere *)
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