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Apparently Worm(3) is about
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Awhile ago I posted a python implementation of linear BEAF. Here's a more condensed version I made yesterday out of inspiration from the Bignum Bakeoff entries. It clocks in at 125 characters which I guess is pretty good for a roughly
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I thought it would be interesting to put the BEAF system into python 3 for the sake of completeness. So far, only linear arrays are supported. Further dimensions might come later. Optimization/obfuscation suggestions are welcome! For inquiries concerning BEAF arrays with two or fewer entries, consult your local calculator.
def beaf(A):
if len(A)

This googological form was created with the intent of implementing a curious little "method" I've been thinking about for some time. It pulls inspiration from various array notations, notably from moments where an entire array itself basically goes into an existing entry. The following characteristics are obviously subject to change, but the key aspects explored in DAN should remain.
On to the mathematics! Consider a modified form of addition, using some arbitrary symbol such as :, whereby the entire expression is more or less inserted into itself, progressively from left to right. During such an insertion, all : operators in the inserted expression become regular + operators. Furthermore, as each term becomes embedded, the preceding : operaâ€¦
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This will be a kind of(?) short article; just wanted to have some discussion over this finding/curiosity.
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I know how familiar the people of this site are with the concept of recursion, and I'm sure a fair amount of you have heard about the primitiverecursive Fibonacci series, in which the first two numbers are given as 0 and 1, or 1 and 1 (as they yield the same result). Further numbers in the sequence are, simply enough, the summation of the two previous entries (1+1=2, 1+2=3, 2+3=5, etc). I'd imagine the sequence's growth rate is absolutely puny, so I'll be quick.
An interesting number emerges as the limit of ratios between consecutive numbers from sufficiently high places in the sequence. The value is approximately 1.618, and is known asâ€¦