Alternating Hexagon Fractal Normalized Chaos Game

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Point color: red green blue yellow cyan magenta white

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\(\mathcal{F} = (\mathbb{R}^2,T_1\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 ,\(R_1T_2\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 ,\(R_2T_1\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 ,\(R_3T_2\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 ,\(R_4T_1\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 ,\(R_5T_2\) R_0 R_1 R_2 R_3 R_4 R_5 FR_0 FR_1 FR_2 FR_3 FR_4 FR_5 )

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Normalization

In a regular chaos game, each function is picked with equal probability, but some functions spread out that probability more so than others, causing dark patches to occur. The probabilities of each function being picked in this chaos game have been weighted so that the entire fractal has uniform brightness.

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