💾 Archived View for tilde.team › ~smokey › fractal_compendium › sirpin › pascals_mod_2.gmi captured on 2024-08-31 at 12:55:45. Gemini links have been rewritten to link to archived content
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scals triangle mod 2
1
1 1
1[2]1
1 3 3 1
1[4][6][4]1
1 5[10][10] 5 1
1[6]15 [20] 15[6]1
1 7 21 35 35 21 7 1
Pascals Triangle Mod 2 red/black
Its kind of hard to see with just ascii but if you look closely you will notice that the structure of numbers looks vaugely like the sierinski triangle and sure enough, yes it is.
I will do the triangle again, this time labeling numbers divisible by 2 "0" and those not divisible by 2 "1". This is what "mod 2" means really, instead of our base 10 numbers, its base 2.
1
1 1
1 0 1
1 1 1 1
1 0 0 0 1
1 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1 1
Can you see it?
1 row 1
1 1 row 2
1 0 1
1 1 1 1 row 4
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1\0 0 0/ 1
1 1\0 0/ 1 1
1 0 1\0/ 1 0 1
1 1 1 1V 1 1 1 1 row 8
Now look at the pictures and see the structure of even and odd (black and red) as the iterations scale up.
Thats right! Its the sierpinski triangle structure. Note that the pattern completes every power of 2.
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