“2DFARCSOD”, which represents “2-Dimensional, Flat And Rectangular Chart of Squares On the Dot”.
Before I start to make a 2DFARCSOD, I need to put some colors on the chessboard to show the process as clear as possible.
My sincere apology to people with color vision deficiency, but color is the best way I can ever imagine to make this chart easier to understand.
(Just for a quick memorize: North is red because it’s crowded. South is blue because it’s iced. West is green because it’s scientific. East is purple because it’s mysterious.)
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| A colored chessboard |
It takes seven steps to make a 2DFARCSOD:
1) Replicate infinite times of chessboard and make them all West-East connected, to create a stream of chessboards. We call it “stream-alpha”.
2) Duplicate the “stream-alpha”.
3) Perform horizontal reflection to a “stream-alpha”, to make it only North-South reversed but not East-West reversed. We call it “stream-beta”.
4) Shift the “stream-beta” by 4 squares, to align rank a with e, b with f, c with g, and d with h.
5) Connect their South borders, to create a new stream. We call it “stream-gamma”.
6) Duplicate the “stream-gamma”, and connect their north borders.
7) Repeat step 6 infinite times, to eventually create a 2DFARCSOD, which is an infinite big, 2-dimensional chessboard continuum without border.
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| The animation of making a 2DFARCSOD |
The relative positions between all squares on 2DFARCSOD are exactly the same as they are on the Dot.
The 2DFARCSOD is an infinite continuum because the surface of the Dot is border-less. The only way to make a border-less 2-dimensional chart is to make it infinite big.
By the way, you can use the same method to create a 2-dimensional, flat and rectangular chart of the surface of terrestrial globe:
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| 2-dimensional, flat and rectangular chart of terrestrial globe |
On the Dot, any piece moves along a single direction will find itself arriving at the very same square where it left from over and over again, because the piece is walking a loop. The same thing happens on the 2DFARCSOD.
To be continued.
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