# The Cantor Sequence with Bits

The Cantor Sequence with Bits

The Cantor sequence is similar to the Cantor set but deals with integers. To construct it, start with the natural numbers , writing them in ternary notation as . Construct a binary sequence : if in ternary has only 0s or 2s, let =1; otherwise let =0. This gives =1,0,1,0,0,0,1,0,1,….

n=0,1,2,3,4,5,6,7,8,9,…

0,1,2,10,11,12,20,21,22,100,…

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This Demonstration shows the Cantor sequence for the numbers from 0 to -1. You can scale and scan the sequence. The pixel colors code the digits: red for -1, green for 0, blue for 1, and gray for 2. Yellow mesh lines mark the bits of the Cantor sequence and purple mesh lines mark the selected position in the selected range. The positions are given as fractions and present the subrange of 81 digit values of integers for the scan.

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