Pascal's triangle

Fractal Figure Produced By Card Games.

  In the last part of this section, we present a very interesting propery of these games. In the previous section, we studied Fractal pattern of Pascal's triangle.
(Remark:Fractal Figure Made by Pascal's Triangle)
  Pascal-like triangles also make Fractal Figures. These Fractal Figures are made by the Game 1 in this section for s=1.

"p players take turns, and each player takes out a card in his or her turn. The player who takes out a red card will be the loser of the game."

In the following Fractal Figures are made by games for p = 4, 6 and 12 respectively.

4人プレイ 4人プレイ 4人プレイ

If you divide numbers by 3 and use the remainder, then you have the following Fractal Figures

for p = 4, 6 and 12.

4人プレイ 4人プレイ 4人プレイ

  As you see, the pattern changes as we change the number p.

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