FractionalGeometry-Chap2

FractionalGeometry-Chap2

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Unformatted text preview: r a moment, consider {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, . . . } 54 CHAPTER 2. ITERATED FUNCTION SYSTEMS and {4, 6, 6, 9, 2, 0, 1, 6, 0, 9, 1, 0, 2, 9, . . . } Are these random sequences? Of course, the ellipsis makes this question impossible to answer. Many would say the first is not, because we recognize it as the first 14 digits in the decimal expansion of π , and assume the remaining digits of the sequence are the remaining digits of π . If this is true, then of course the sequence is not random in our sense, because we have just given a specification more compact than listing the entire (infinite) sequence. (An undergraduate classmate of mine decided to memorize the first 200 digits of the decimal expansion of π , to impress people at parties, he said, though which people would be impressed by this never was so clear to me. He used an old book from the library, eventually seen to have a mistake in the 20th digit. So he had memorized 200 digits of some real number – in fact, of infinitely many real numbers – but not π . But until he learned of the mistake in the book, he thought his 200...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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