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The picture was made by making a semicircle with a radius of half the big circle then one with 2/3 of the radius then the circle was rotated and the pattern was repeated.

In a three colour circle 1/3 of the circle would be red and in a four colour circle 1/4 would be red. The proportion of red in a n colour circle would be 1/n. The proportion of any other colour in a n colour circle would also be 1/n. I am yet to prove it.