2 ms·

I came up with a slightly different take on irrational radices is to give a finite closed form representation of integers in an irrational base, code and write

• graderjs 4y ago
  Basically my ideas is: N = kb + r N - integer k - divisor r - remainder b - base So N can be written has a multiple of b plus the remainder. Now, iterate with k. k = k_2b + r_2 And so on, as every number can be written like this. You end up with a polynomial in b N = b^j.r_j + b^(j-1).r_{j-1} + ... + b.r_1 + r_0 Which is represented as a "numeral" by its coefficients (r_j..r_0) One interesting property of this rep, is that for base phi (Golden Ratio ~ 1.618: (1+5^(0.5)/2)) no rep has a "101" subsequence. So basically then integers coded into base-phi get like a multipart/form-data or MIME encoding for free with the "boundary" being, the nonexistant sequence: 101. I really loved to discover this! :) ;p xx ;p
  • pyinstallwoes 4y ago
    I’m so glad someone finally worked on something like this. I’ve been compiling research in this direction for years. I have various ideas but haven’t had the motivation to see it through lately. It’d be interesting to optimize hardware on this direction. Have you seen this? https://neuraloutlet.wordpress.com/tag/ternary-tau-system/ https://neuraloutlet.wordpress.com/tag/ternary-tau-system/ The properties of such a system are remarkable.