Julian, do you see any way to lengthen the nonrandomness? --Bill On Wed, Mar 19, 2014 at 5:12 PM, Julian Ziegler Hunts <julianj.zh@gmail.com>wrote:
What's strange about this? Other than the long runs of identical bits, which are easily explained by rewriting it as 1+Sqrt[1+(Sqrt[1+4^(1-k)]-1)/2]/2^(k/2+1/2) (which accurately predicts a lack of structure for k even), and noting that the series coefficients for sqrt(1+x) have power-of-two denominators (and therefore so do the coefficients of sqrt(1+(sqrt(1+x)-1)/2)).
Julian
On Tue, Mar 18, 2014 at 4:52 PM, Bill Gosper <billgosper@gmail.com> wrote:
Nice. But your plots are line-wrapped. Out[698]= 1 + 2^(-1 - k) Sqrt[2^k + 2 Sqrt[1 + 2^(2 (-1 + k))]]
You have, e.g. In[700]:= ArrayPlot[ Partition[RealDigits[%698 /. k -> 63, 2, 63^2][[1]], 63]]
Try In[705]:= ArrayPlot[ Partition[ Join[ConstantArray[0, 32], RealDigits[%698 /. k -> 63, 2, 2*63^2][[1]]], 2*63]] --rwg Violating two embargoes at once: Climate change makes planes disappear.