23 Nov
2016
23 Nov
'16
8:29 p.m.
x xor <non dyadic-rational>: Discontinuous at the dyadic rationals. Continuous everywhere else? --rwg Date: 2016-11-23 02:51 From: Joerg Arndt <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> * Bill Gosper <billgosper@gmail.com> [Nov 23. 2016 10:21]:
[...] He says it's really just prf dressed up. And he makes the remarkable observation that the frac4 dragon gosper.org/4flopfour.png is the bar graph of x xor 2/3 ! gosper.org/xor667fade.png It appears that x xor r makes a fractile for every rational r. --rwg
Correct: write 1 in binary as 0.11111..., then observe that (x xor r) + ((1-x) xor r) == 1. Best regards, jj