/* f(z)=1/(z3+dz+c) mit c=0,37 und d=2,1, dargestellt auf [-2,1;2,1]x[-2,1;2,1]. https://web.archive.org/web/20161024194536/http://www.ijon.de/mathe/julia/some_julia_sets_3.html https://fractalforums.org/fractal-mathematics-and-new-theories/28/rational-function/4279/45 f(z) := 1/{z^3 + 2.099609375*z +0.349609375} The parameters used here differ slightly from the ones on the site, as I prefer working with exactly double-representable numbers by using a near dyadic fraction, hoping the overall structure of the set remains the same (i.e. intersecting Jordan curves). */ kill(all); remvalue(all); display2d:false; /* map */ a: 2.1; /* d */ c: 0.37; define(f(z), 1/(z^3+ a*z + c)); /* first derivativa wrt z */ define( d(z), diff(f(z),z,1)); GiveOrbit(z0,iMax):= /* computes (without escape test) (forward orbit of critical point ) and saves it to the list for draw package */ block( [z,orbit,temp], z:z0, /* first point = critical point z:0+0*%i */ orbit:[[realpart(z),imagpart(z)]], for i:1 thru iMax step 1 do ( z:f(z), z:float(z), z:rectform(z), z:float(z), if (cabs(z)>3) then break, /*if (cabs(z)< 0.00001) then break, */ orbit:endcons([realpart(z),imagpart(z)],orbit)), return(orbit) )$ /* critical points [-0.8366600265340756*%i,0.8366600265340756*%i] */ s:solve(d(z)=0); s : map(rhs,s); s : map('float,s); orbits:[]; for z in s do ( print(i,z), orbit : GiveOrbit(z,20), orbits:endcons(orbit,orbits) )$ path:"~/Dokumenty/ijon/3006/"; plot2d( [discrete, orbits[1]] ); /* orbits[1] [[0,-0.8366600265340756], [0.2452117436543176,0.7762767825221721], [0.2396260928745842,-0.6838310760652884], [0.3015963408933682,0.675715442389246], [0.3001016881090526,-0.6291282780397109], [0.3366250782337031,0.6232467109929899], [0.3350520554545808,-0.5927029946423565], [0.3605584519118678,0.5878748450784567], [0.3589115311530886,-0.5654176406159377], [0.3782956328318648,0.5612780934184168], [0.3766528969333711,-0.5436696817753796], [0.3921606472131179,0.5400336800431285], [0.3905628214083765,-0.5256429846342945], [0.4034076920661117,0.5223966937225157], [0.401872360484979,-0.5102891501449793], [0.4127822170404693,0.5073554505102452], [0.4113153307114809,-0.4969470635077123], [0.4207599219945199,0.4942705604062732], [0.4193617757264228,-0.4851727874545359], [0.4276612044735157,0.4827120563253007], [0.4263294162446253,-0.4746537974662441]] (%i17) orbits[2]; [[0,0.8366600265340756],[0.2452117436543176,-0.7762767825221721], [0.2396260928745842,0.6838310760652884], [0.3015963408933682,-0.675715442389246], [0.3001016881090526,0.6291282780397109], [0.3366250782337031,-0.6232467109929899], [0.3350520554545808,0.5927029946423565], [0.3605584519118678,-0.5878748450784567], [0.3589115311530886,0.5654176406159377], [0.3782956328318648,-0.5612780934184168], [0.3766528969333711,0.5436696817753796], [0.3921606472131179,-0.5400336800431285], [0.3905628214083765,0.5256429846342945], [0.4034076920661117,-0.5223966937225157], [0.401872360484979,0.5102891501449793], [0.4127822170404693,-0.5073554505102452], [0.4113153307114809,0.4969470635077123], [0.4207599219945199,-0.4942705604062732], [0.4193617757264228,0.4851727874545359], [0.4276612044735157,-0.4827120563253007], [0.4263294162446253,0.4746537974662441]] */