Image:Pm1234 Ground.png
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[edit] Summary
Terms and partial sums of 1 − 2 + 3 − 4 + · · · going out to the horizon.
- The terms are indicated as black lines executing displacements to the camera's right, plus a constant displacement away from the camera.
- The partial sums are where the terms end; they are indicated as black circles.
- The action takes place on an infinite horizontal plane. The integers are located on the gray lines. The horizon is picked out by a bluish sky.
- The camera type is rectangular perspective. Of course, it is placed over x = 1/4 for symmetry.
[edit] POV-Ray source
Warning: this scene requires a lot of antialiasing, and it is slow.
camera {
location <.25, 4, -4.5>
up y*image_height right x*image_width angle 65 look_at <.25, 0, 10>
}
background { rgb 1 }
#declare an = 0;
#declare sn = 0;
#declare snn = 0;
union {
#declare n=1;
#while (n<15000)
#declare an = n * pow(-1, n+1);
#declare snn = sn;
#declare sn = sn + an;
cylinder { 0, z*sqrt(1+an*an), .1 scale <1, 0.3/sqrt(n), 1>
rotate y*degrees(atan(an)) translate <snn, 0, n>
}
sphere { <snn, 0, n>, .2 scale <1, 0.3/sqrt(n), 1> }
#declare n=n+1;
#end
pigment { color rgb 0 }
}
intersection {
plane { y, .01/(n*n) pigment { color rgb 0 } }
plane { -z, -n }
plane { -x, 0 rotate y*-degrees (atan (.5)) translate <0, 0, 1> }
plane { x, 0 rotate y*degrees (atan (.5)) translate <1, 0, 2> }
pigment { color rgbt 1 }
}
plane {
y, 0
pigment {
gradient x
color_map {
[0 rgbt .5]
[0.024 rgbt .5]
[0.025 rgbt 1]
[0.975 rgbt 1]
[0.976 rgbt .5]
[1 rgbt .5]
}
}
}
plane { -y, -5 pigment { color rgbf <.9, .9, 1, .9> } }
[edit] Licensing
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