D:=Dragon[Thue] d:=Dragon[1-Thue] Then Im[D] + Re[D] == 7/15 + Abs[D]^2, Im[d] + Re[d] == 7/15 + Abs[d]^2, D + I d == I, 113/15 + 15 Abs[d]^4 + 15 Abs[D]^4 == 16 Abs[d]^2 + 16 Abs[D]^2 . Test: D ~ (552141176700154938708639716987262633 + 449568033846806255846939851654337899 I)/ 1329227995784915872903807060280344576 d ~ (879659961938109617056867208626006677 + 552141176700154938708639716987262633 I)/ 1329227995784915872903807060280344576 In[258]:= {Im[D] + Re[D] | 7/15 + Abs[D]^2, Im[d] + Re[d] | 7/15 + Abs[d]^2, D + I d | I, 113/15 + 15 Abs[d]^4 + 15 Abs[D]^4 | 16 Abs[d]^2 + 16 Abs[D]^2} /. {D -> (552141176700154938708639716987262633 + 449568033846806255846939851654337899 I)/ 1329227995784915872903807060280344576., d -> (879659961938109617056867208626006677 + 552141176700154938708639716987262633 I)/ 1329227995784915872903807060280344576.} Out[258]= {0.753602251625348009164368437081203650 | 0.753602251625348009164368437081203650, 1.077167455980927276355373650781728282 | 1.077167455980927276355373650781728282, 0.*10^-37 + 1.000000000000000000000000000000000000 I | I, 14.3589819883670712349825400724735776 | 14.3589819883670712349825400724735776} It's a little disappointing that we don't get valuations of Dragon[Thue] and Dragon[1-Thue] in terms of Thue, the way we do with Hilbert[Thue] = Thue + I and Hilbert[1-Thue] = 1 - Thue + I, which follow from treating Hilbert[t] as a four(?) state automaton that produces one bit of x and one bit of y for every two bits of t. —rwg Unlike the superfluous constant Glaisher, Thue (or a similar name) deserves a definition in Mathematica.