Home Follow the rabbit Papers Software NET map documentation Thanks Gallery of pullback maps NET maps of degree 2 Dynamic portraits
Notes Nontrivial cycles Rationality degree 2 (16 portraits) degree 3 (94 portraits) degree 4 (272 portraits) degree 5 (144 portraits) degree 6 (338 portraits) degree 7 (152 portraits) degree 8 (476 portraits) degree 9 (153 portraits) degree 10 (353 portraits) degree 11 (153 portraits) degree 12 (483 portraits) degree 13 (153 portraits) degree 14 (353 portraits) degree 15 (153 portraits) degree 16 (483 portraits) degree 17 (153 portraits) degree 18 (353 portraits) degree 19 (153 portraits) degree 20 (483 portraits) degree 21 (153 portraits) degree 22 (353 portraits) degree 23 (153 portraits) degree 24 (483 portraits) degree 25 (153 portraits) degree 26 (353 portraits) degree 27 (153 portraits) degree 28 (483 portraits) degree 29 (153 portraits) degree 30 (353 portraits) degree 31 (153 portraits) degree 32 (483 portraits) degree 33 (153 portraits) degree 34 (353 portraits) degree 35 (153 portraits) degree 36 (483 portraits) degree 37 (153 portraits) degree 38 (353 portraits) degree 39 (153 portraits) degree 40 (483 portraits)
Hurwitz classes
Notes m=2, n=1 (4 classes) m=3, n=1 (9 classes) m=4, n=1 (24 classes) m=2, n=2 (10 classes) m=5, n=1 (25 classes) m=6, n=1 (88 classes) m=7, n=1 (47 classes) m=8, n=1 (133 classes) m=4, n=2 (85 classes) m=9, n=1 (120 classes) m=3, n=3 (43 classes) m=10, n=1 (269 classes) m=11, n=1 (140 classes) m=12, n=1 (618 classes) m=6, n=2 (201 classes) m=13, n=1 (228 classes) m=14, n=1 (583 classes) m=15, n=1 (646 classes) m=16, n=1 (789 classes) m=8, n=2 (503 classes) m=4, n=4 (155 classes) m=17, n=1 (469 classes) m=18, n=1 (1,544) m=6, n=3 (457) m=19, n=1 (629) m=20, n=1 (1,935) m=10, n=2 (621) m=21, n=1 (1,505) m=22, n=1 (1,902) m=23, n=1 (1,079) m=24, n=1 (3,976) m=12, n=2 (2,284) m=25, n=1 (1,678) m=5, n=5 (332) m=26, n=1 (3,037) m=27, n=1 (2,562) m=9, n=3 (1,032) m=28, n=1 (4,472) m=14, n=2 (1,384) m=29, n=1 (2,116) m=30, n=1 (8,521)
The zoo
Notes airplane corabbit rabbit Lodge's cubic Newton maps f1/4 z2 + i basilica mate basilica
  • PORTRAIT 1 (a->a, b->b, c->c, d->d)
    {} critical. 1, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 2 (a->b, b->a, c->c, d->d)
    {} critical. 1, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 3 (a->b, b->a, c->d, d->c)
    {} critical. 1, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 4 (a->b, b->c, c->a, d->d)
    {} critical. 1, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 5 (a->b, b->c, c->d, d->a)
    {} critical. 1, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 6 (a->a, b->b, c->c, d->d)
    {a} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 7 (a->b, b->a, c->c, d->d)
    {a} critical. 1, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 8 (a->b, b->a, c->d, d->c)
    {a} critical. 1, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 9 (a->b, b->c, c->a, d->d)
    {a} critical. 1, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 10 (a->b, b->c, c->d, d->a)
    {a} critical. 1, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 11 (a->c, b->c, c->d, d->a)
    {a} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 12 (a->c, b->c, c->a, d->d)
    {a} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 13 (a->c, b->c, c->a, d->b)
    {a} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 14 (a->a, b->a, c->d, d->c)
    {a} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 15 (a->a, b->a, c->c, d->d)
    {a} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 16 (a->a, b->a, c->b, d->d)
    {a} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 17 (a->a, b->a, c->b, d->c)
    {a} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 18 (a->c, b->c, c->d, d->a)
    {b} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 19 (a->c, b->c, c->a, d->d)
    {b} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 20 (a->c, b->c, c->a, d->b)
    {b} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 21 (a->a, b->a, c->d, d->c)
    {b} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 22 (a->a, b->a, c->c, d->d)
    {b} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 23 (a->a, b->a, c->b, d->d)
    {b} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 24 (a->a, b->a, c->b, d->c)
    {b} critical. 0, 1, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 25 (a->b, b->a, c->c, d->d)
    {c} critical. 1, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 26 (a->b, b->c, c->a, d->d)
    {d} critical. 1, 1, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 27 (a->a, b->b, c->c, d->d)
    {ab} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 28 (a->b, b->a, c->c, d->d)
    {ab} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 29 (a->b, b->a, c->d, d->c)
    {ab} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 30 (a->b, b->c, c->a, d->d)
    {ab} critical. 1, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 31 (a->b, b->c, c->d, d->a)
    {ab} critical. 1, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 32 (a->b, b->a, c->c, d->d)
    {ac} critical. 1, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 33 (a->b, b->a, c->d, d->c)
    {ac} critical. 1, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 34 (a->b, b->c, c->d, d->a)
    {ac} critical. 1, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 35 (a->c, b->c, c->d, d->a)
    {ac} critical. 1, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 36 (a->c, b->c, c->a, d->d)
    {ac} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 37 (a->c, b->c, c->a, d->b)
    {ac} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 38 (a->a, b->a, c->d, d->c)
    {ac} critical. 0, 1, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 39 (a->a, b->a, c->c, d->d)
    {ac} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 40 (a->a, b->a, c->b, d->d)
    {ac} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 41 (a->a, b->a, c->b, d->c)
    {ac} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 42 (a->c, b->c, c->a, d->a)
    {ac} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 43 (a->a, b->a, c->c, d->c)
    {ac} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 44 (a->a, b->a, c->b, d->b)
    {ac} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 45 (a->b, b->c, c->a, d->d)
    {ad} critical. 1, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 46 (a->c, b->c, c->d, d->a)
    {ad} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 47 (a->c, b->c, c->a, d->d)
    {ad} critical. 1, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 48 (a->c, b->c, c->a, d->b)
    {ad} critical. 1, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 49 (a->a, b->a, c->b, d->d)
    {ad} critical. 0, 1, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 50 (a->a, b->a, c->b, d->c)
    {ad} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 51 (a->c, b->c, c->a, d->a)
    {ad} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 52 (a->a, b->a, c->c, d->c)
    {ad} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 53 (a->c, b->c, c->d, d->a)
    {bc} critical. 1, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 54 (a->c, b->c, c->a, d->d)
    {bc} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 55 (a->c, b->c, c->a, d->b)
    {bc} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 56 (a->a, b->a, c->d, d->c)
    {bc} critical. 0, 1, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 57 (a->a, b->a, c->c, d->d)
    {bc} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 58 (a->a, b->a, c->b, d->d)
    {bc} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 59 (a->a, b->a, c->b, d->c)
    {bc} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 60 (a->a, b->a, c->b, d->b)
    {bc} critical. 0, 0, 1, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 61 (a->c, b->c, c->d, d->a)
    {bd} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 62 (a->c, b->c, c->a, d->d)
    {bd} critical. 1, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 63 (a->c, b->c, c->a, d->b)
    {bd} critical. 1, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 64 (a->a, b->a, c->b, d->d)
    {bd} critical. 0, 1, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 65 (a->a, b->a, c->b, d->c)
    {bd} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 66 (a->c, b->c, c->a, d->a)
    {bd} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 67 (a->a, b->a, c->c, d->c)
    {bd} critical. 0, 1, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 68 (a->b, b->a, c->c, d->d)
    {cd} critical. 1, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 69 (a->a, b->b, c->c, d->d)
    {abc} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 70 (a->b, b->a, c->c, d->d)
    {abc} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 71 (a->b, b->a, c->d, d->c)
    {abc} critical. 0, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 72 (a->b, b->c, c->a, d->d)
    {abc} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 73 (a->b, b->c, c->d, d->a)
    {abc} critical. 1, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 74 (a->b, b->c, c->a, d->d)
    {abd} critical. 1, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 75 (a->b, b->a, c->c, d->d)
    {acd} critical. 1, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 76 (a->c, b->c, c->d, d->a)
    {acd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 77 (a->c, b->c, c->a, d->d)
    {acd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 78 (a->c, b->c, c->a, d->b)
    {acd} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 79 (a->a, b->a, c->d, d->c)
    {acd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 80 (a->a, b->a, c->c, d->d)
    {acd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 81 (a->a, b->a, c->b, d->d)
    {acd} critical. 0, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 82 (a->a, b->a, c->b, d->c)
    {acd} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 83 (a->c, b->c, c->d, d->a)
    {bcd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 84 (a->c, b->c, c->a, d->d)
    {bcd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 85 (a->c, b->c, c->a, d->b)
    {bcd} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 86 (a->a, b->a, c->d, d->c)
    {bcd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 87 (a->a, b->a, c->c, d->d)
    {bcd} critical. 0, 1, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 88 (a->a, b->a, c->b, d->d)
    {bcd} critical. 0, 0, 1, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 89 (a->a, b->a, c->b, d->c)
    {bcd} critical. 0, 0, 0, 1 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 90 (a->a, b->b, c->c, d->d)
    {abcd} critical. 0, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 91 (a->b, b->a, c->c, d->d)
    {abcd} critical. 0, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 92 (a->b, b->a, c->d, d->c)
    {abcd} critical. 0, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 93 (a->b, b->c, c->a, d->d)
    {abcd} critical. 0, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d
  • PORTRAIT 94 (a->b, b->c, c->d, d->a)
    {abcd} critical. 0, 0, 0, 0 number of nonpostcritical, critical preimages for a, b, c, d