File:Conway's constant.svg
Summary
| Description |
English: The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic scale) tend to straight lines whose slopes coincide with Conway's constant. |
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Plotted in Maple and converted to SVG format in Inkscape, using the following Maple code: > with(plots); > f := proc (n) options operator, arrow; `mod`(n, 10) end proc; > g := proc (n) options operator, arrow; `mod`(floor((1/10)*n), 10) end proc; > h := proc (n) if 1 <= evalf(log10(n)) then if f(n) = g(n) then return 1+h(floor((1/10)*n)) else return 1 end if else return 1 end if end proc; > k := proc (n) if 0 < n then return f(n)+10*h(n)+10^(floor(log10(f(n)+10*h(n)))+1)*k(floor(n/10^h(n))) else return 0 end if end proc; > sequence := proc (N) local i; for i to 19 do N[i+1] := [][i][2])] end do end proc; > sequencedigits := proc (N) local i; for i to 20 do N[i][2] := floor(log10(N[i][2])) end do end proc; > AA := vector(20); AA[1] := [1, 23]; sequence(AA); sequencedigits(AA); a := logplot(AA, color = red); > BB := vector(20); BB[1] := [1, 1]; sequence(BB); sequencedigits(BB); b := logplot(BB, color = blue); > CC := vector(20); CC[1] := [1, 13]; sequence(CC); sequencedigits(CC); c := logplot(CC, color = violet); > DD := vector(20); DD[1] := [1, 312]; sequence(DD); sequencedigits(DD); d := logplot(DD, color = green); > display(a, b, c, d, view = [1 .. 20, 1 .. 10000]); |
| Author | Sandrobt |
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