Gaussian-like distribution

g.rb

def g(n, center, amplitude, total, density)
  Math.sinh(density*((n.to_f - total / 2.0))/(total/2.0))/Math.sinh(density) * amplitude + center
end

N = 30
Density = 10
prev_value = nil
(0..N).each do |n|
  value = g(n, 35, 10, N, Density)
  print "%3d %.4f" % [n, value]
  print " [%+.4f]" % (value - prev_value) if prev_value
  prev_value = value
  puts
end

output - Density 0.2

  0 25.0000
  1 25.6747 [+0.6747]
  2 26.3477 [+0.6730]
  3 27.0191 [+0.6715]
  4 27.6892 [+0.6700]
  5 28.3579 [+0.6687]
  6 29.0255 [+0.6676]
  7 29.6920 [+0.6665]
  8 30.3576 [+0.6656]
  9 31.0223 [+0.6647]
 10 31.6863 [+0.6640]
 11 32.3498 [+0.6634]
 12 33.0127 [+0.6630]
 13 33.6754 [+0.6626]
 14 34.3377 [+0.6624]
 15 35.0000 [+0.6623]
 16 35.6623 [+0.6623]
 17 36.3246 [+0.6624]
 18 36.9873 [+0.6626]
 19 37.6502 [+0.6630]
 20 38.3137 [+0.6634]
 21 38.9777 [+0.6640]
 22 39.6424 [+0.6647]
 23 40.3080 [+0.6656]
 24 40.9745 [+0.6665]
 25 41.6421 [+0.6676]
 26 42.3108 [+0.6687]
 27 42.9809 [+0.6700]
 28 43.6523 [+0.6715]
 29 44.3253 [+0.6730]
 30 45.0000 [+0.6747]

output - Density 1

$ ruby gaussian-like.rb 
  0 25.0000
  1 25.8538 [+0.8538]
  2 26.6669 [+0.8131]
  3 27.4429 [+0.7761]
  4 28.1854 [+0.7425]
  5 28.8976 [+0.7122]
  6 29.5826 [+0.6850]
  7 30.2435 [+0.6609]
  8 30.8833 [+0.6398]
  9 31.5048 [+0.6215]
 10 32.1108 [+0.6060]
 11 32.7039 [+0.5931]
 12 33.2868 [+0.5829]
 13 33.8621 [+0.5753]
 14 34.4323 [+0.5702]
 15 35.0000 [+0.5677]
 16 35.5677 [+0.5677]
 17 36.1379 [+0.5702]
 18 36.7132 [+0.5753]
 19 37.2961 [+0.5829]
 20 37.8892 [+0.5931]
 21 38.4952 [+0.6060]
 22 39.1167 [+0.6215]
 23 39.7565 [+0.6398]
 24 40.4174 [+0.6609]
 25 41.1024 [+0.6850]
 26 41.8146 [+0.7122]
 27 42.5571 [+0.7425]
 28 43.3331 [+0.7761]
 29 44.1462 [+0.8131]
 30 45.0000 [+0.8538]

output - Density 5

  0 25.0000
  1 27.8350 [+2.8350]
  2 29.8665 [+2.0315]
  3 31.3223 [+1.4558]
  4 32.3656 [+1.0434]
  5 33.1136 [+0.7479]
  6 33.6499 [+0.5364]
  7 34.0349 [+0.3850]
  8 34.3117 [+0.2767]
  9 34.5112 [+0.1996]
 10 34.6560 [+0.1447]
 11 34.7621 [+0.1062]
 12 34.8416 [+0.0795]
 13 34.9034 [+0.0617]
 14 34.9542 [+0.0509]
 15 35.0000 [+0.0458]
 16 35.0458 [+0.0458]
 17 35.0966 [+0.0509]
 18 35.1584 [+0.0617]
 19 35.2379 [+0.0795]
 20 35.3440 [+0.1062]
 21 35.4888 [+0.1447]
 22 35.6883 [+0.1996]
 23 35.9651 [+0.2767]
 24 36.3501 [+0.3850]
 25 36.8864 [+0.5364]
 26 37.6344 [+0.7479]
 27 38.6777 [+1.0434]
 28 40.1335 [+1.4558]
 29 42.1650 [+2.0315]
 30 45.0000 [+2.8350]