Sierpiski Tringle

The Sierpiski Triangle is obtained as the residual set remaining when one begins with a triangle and applies the operation of dividing it into four equal triangles and omitting the interior of the center one, then repeats this operation on each of the surviving 3 triangles, then repeats again on the surviving 9 triangles, and so on $\cdots$ . See [36, Example 2.7].

The Sierpiski Triangle is homeomorphic to the unique nonempty compact set K of the complex plane that satisfies

$$K= w_1(K) \cup w_2(K) \cup w_3(K) \quad ,$$

where w₁, w₂, w₃ are maps of the complex plane defined by w₁(z)=z/2, w₂=(z + 1)/2 and w₃=(z+i)/2.

Figure ( A ) Sierpiski Tringle


Figure ( B ) Sierpiski Tringle


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