[Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org]

If you want to see the first miracle, concerning FOUR general points in the plane
(taking place in the plane), as well as the
the first miracle, concerning FIVE general points in the plane,
as well as the Pascal miracle concerning SIX points on a conic
the input yields
the output

If you want to see the beginning of the sequence enumerating
the successive generations (alternating between points and lines), if they were FOUR initial points (i.e. four Adams),
from the 0th generation all the way to the 7th
the input yields
the output
This took less than tree seconds!
[Added July 2, 2014: but to get the next term, took much longer! (about 1.5*10^{6} seconds),
if you want also to see the number of creatures born in the 8thgeneration (all males, of course)
the input yields
the output
]

If you want to see the beginning of the sequence enumerating
the successive generations (alternating between points and lines), if they were FIVE initial points (i.e. five Adams),
from the 0th generation all the way to the 4th
the input yields
the output

If you want to see the beginning of the sequence enumerating
the successive generations (alternating between points and lines), if they were SIX initial points (i.e. six Adams),
from the 0th generation all the way to the 4th
the input yields
the output

If you want to see the beginning of the sequence enumerating
the successive PURE (where intergenerational mating is forbidden)
generations (alternating between points and lines), if they were FIVE initial points (i.e. five Adams),
from the 0th generation all the way to the 4th
the input yields
the output

If you want to see two detailed different genealogies of the same Pascal line for six
points on a conic,
the input yields
the output

If you want to see a detailed genealogy for a random 12th generation object
(that happens to be a line) staring with four initial ("Adams") random points
the input yields
the output

If you want to see a picuture of a 4generation points
the input yields
the output

If you want to see 100 random 9generation lines
the input yields
the output