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{ version = 1.48; (* of sphere.p 2014 Dec 06} (* begin module describe.sphere *) (* name sphere: plot density of Shannon spheres synopsis sphere(spherep: in, sigma: out, xyin: out, output:out) files 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 description 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. documentation [1988 jan 23,5] @article{Schneider.ccmm, 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 {https://alum.mit.edu/www/toms/papers/ccmm/} {https://alum.mit.edu/www/toms/papers/ccmm/}", year = 1991} see also Schneider.ccmm paper: https://alum.mit.edu/www/toms/paper/ccmm example parameters: spherep example plotting file for xyplo: sphere.xyplop plotting program: xyplo.p resulting graph, postscript ... : sphereinteger.ps resulting graph, jpg .......... : example of fractal graph parameters: spherep.fractal resulting graph, postscript ... : spherefractal.ps resulting graph, jpg .......... : Related programs: compress D dimensional sphere to 2D: ... ring.p plot output of ring: ................... riden.p Match fdr curve: ....................... fdr.p author Thomas Dana Schneider bugs none known *) (* end module describe.sphere *) {This manual page was created by makman 1.45}{created by htmlink 1.62}