Complex power tower

log.txt

> c=new C(-0.8); x=c; res=[]; for (let i = 0; i < 10; i++) res.push(x = x.pow(c)); res
[ { re: -0.967131781178879, im: -0.7026623692120304 },
  { re: -0.3691153675094393, im: 0.7844100843322339 },
  { re: -0.042251892773906244, im: -1.120235261735242 },
  { re: 0.2557231881056781, im: 0.8760941991244778 },
  { re: 0.5543917466943977, im: -0.9220211474369996 },
  { re: 0.6410070262045503, im: 0.6918834867768658 },
  { re: 0.8285847445893876, im: -0.6415296186745002 },
  { re: 0.8325254334492322, im: 0.4845217029269798 },
  { re: 0.940151752960039, im: -0.4217163364065653 },
  { re: 0.9213022157809088, im: 0.32312929583602706 } ]
> c=new C(-1.1); x=c; res=[]; for (let i = 0; i < 10; i++) res.push(x = x.pow(c)); res
[ { re: -0.8563954906892556, im: 0.278259762689984 },
  { re: -1.1216847051398382, im: -0.035250361960482375 },
  { re: -0.8466510953811415, im: -0.24309316387515723 },
  { re: -1.149723951763776, im: -0.007585235122412489 },
  { re: -0.8176254871746789, im: -0.2591179454539053 },
  { re: -1.1836148835722948, im: 0.02774089060791012 },
  { re: -0.7962003910623191, im: 0.2361947851059457 },
  { re: -1.2266675056988694, im: -0.0037558561815327243 },
  { re: -0.7604612351861079, im: -0.24426027944425033 },
  { re: -1.2799564554044862, im: 0.03547810243115621 } ]
> c=new C(0, 1); x=c; res=[]; for (let i = 0; i < 10; i++) res.push(x = x.pow(c)); res
[ { re: 0.20787957635076193, im: 0 },
  { re: 6.123233995736766e-17, im: -1 },
  { re: 4.810477380965351, im: 0 },
  { re: 6.123233995736766e-17, im: 1 },
  { re: 0.20787957635076193, im: 0 },
  { re: 6.123233995736766e-17, im: -1 },
  { re: 4.810477380965351, im: 0 },
  { re: 6.123233995736766e-17, im: 1 },
  { re: 0.20787957635076193, im: 0 },
  { re: 6.123233995736766e-17, im: -1 } ]
> c=new C(0, 1.3); x=c; res=[]; for (let i = 0; i < 10; i++) res.push(x = x.pow(c)); res
[ { re: 0.12228941134484532, im: 0.04340604121591821 },
  { re: -0.567247828878551, im: -0.30034226515486406 },
  { re: 26.43810103903382, im: -17.186235006487614 },
  { re: -0.47414341829233714, im: -2.0617837939786496 },
  { re: 5.8090457343663395, im: 8.552283822602723 },
  { re: -0.2802988617612534, im: 0.02952395957970702 },
  { re: -0.0014557849568851656, im: -0.019245134665599368 },
  { re: 3.46287293725017, im: 7.763750119067718 },
  { re: -0.20958449053540218, im: 0.07873294037976344 },
  { re: -0.009835394509808823, im: -0.02500034903428348 } ]
> c=new C(0, 1.3); x=c; res=[]; for (let i = 0; i < 30; i++) res.push(x = x.pow(c)); res
[ { re: 0.12228941134484532, im: 0.04340604121591821 },
  { re: -0.567247828878551, im: -0.30034226515486406 },
  { re: 26.43810103903382, im: -17.186235006487614 },
  { re: -0.47414341829233714, im: -2.0617837939786496 },
  { re: 5.8090457343663395, im: 8.552283822602723 },
  { re: -0.2802988617612534, im: 0.02952395957970702 },
  { re: -0.0014557849568851656, im: -0.019245134665599368 },
  { re: 3.46287293725017, im: 7.763750119067718 },
  { re: -0.20958449053540218, im: 0.07873294037976344 },
  { re: -0.009835394509808823, im: -0.02500034903428348 },
  { re: -0.13046850865445384, im: 12.543939829873025 },
  { re: -0.1266505333736279, im: -0.018686461003336086 },
  { re: -43.78031947184452, im: -22.204218648710086 },
  { re: 11.042564949214503, im: -30.313318483689173 },
  { re: -0.9545790023478862, im: -4.799417734910906 },
  { re: -4.711678100436234, im: 8.760264039196805 },
  { re: -0.06750034032161806, im: 0.01055716454740112 },
  { re: -0.019373712393563, im: 0.0070063424234936755 },
  { re: 0.00868464655375915, im: 0.024970684615711176 },
  { re: 0.0020970045887601127, im: 0.20049427203022888 },
  { re: -0.06515359652067883, im: -0.11427147808078406 },
  { re: -13.231004840160502, im: -7.3077410988608715 },
  { re: -28.516828108095993, im: -11.681979727410091 },
  { re: -9.06806453506793, im: -34.65779848304561 },
  { re: -0.6462977577125014, im: -10.728520371159485 },
  { re: -8.320899773413437, im: 0.45361086936081113 },
  { re: -0.01674933029469194, im: 0.0067923129230433 },
  { re: 0.013439678340958086, im: 0.02431926911443943 },
  { re: -0.013548930113332634, im: 0.24977841147844304 },
  { re: -0.027645088448773725, im: -0.1177352005660586 } ]
> c=new C(0, 3); x=c; res=[]; for (let i = 0; i < 30; i++) res.push(x = x.pow(c)); res
[ { re: -0.008876640735623678, im: -0.0013801328997494863 },
  { re: 4.299225213345099e-12, im: -7801.297332492359 },
  { re: -47.687771468940994, im: 100.58590487857981 },
  { re: 1.399652945722438e-17, im: 0.0023802967438898886 },
  { re: 0.006706292276008066, im: 0.005977052909173721 },
  { re: 6.062688409449255e-15, im: -0.11260189727404255 },
  { re: 107.32910961590719, im: -29.53150922268058 },
  { re: 1.0864671859905047e-12, im: 2.237847579961147 },
  { re: -0.006723695351370002, im: 0.005957469126441625 },
  { re: 3.1048852618775642e-15, im: -0.0007104368333266124 },
  { re: -108.06718826693833, im: -26.704505755955477 },
  { re: 2.3565093098596626e-7, im: 5990.959761854039 },
  { re: 0.005142651215499325, im: 0.007365640234567094 },
  { re: 1.9795966753238915e-11, im: -0.05591911893975375 },
  { re: -79.66541505375334, im: -77.75004453959654 },
  { re: 0.000003881128544743827, im: 1218.1450265873325 },
  { re: -0.007008290557134038, im: 0.0056199094814587194 },
  { re: 1.7578627176067233e-11, im: -0.0006130323617249677 },
  { re: -109.09595071919921, im: 22.129600371834957 },
  { re: 3.796303808295527e-11, im: 0.00014710143035350212 },
  { re: 0.0020512518500594512, im: -0.008745970979637351 },
  { re: 0.00012953944186822115, im: -55.77190089413365 },
  { re: 97.55291304197618, im: -53.618133837957416 },
  { re: 0.000094407458734674, im: 4.516242187872079 },
  { re: -0.0016909297904832618, im: -0.008823287159428728 },
  { re: 0.036960233225756894, im: -196.45500808595312 },
  { re: -110.26744306564679, im: -14.790497602734456 },
  { re: 14.064369100518052, im: 8306.264136379616 },
  { re: -0.003271457031410016, im: 0.008415528429904251 },
  { re: 0.00004501062625072634, im: -0.002953417357817942 } ]
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