Divergence angle |
Reduction rate |
number of Dots |
---|---|---|

18.0° |
2.00% |
128 |

[ a / z ] |
[ s / x ] |
[ d / c ] |

Presets:

Div ° | Red % | Dots | Parastichies |

173.6 | 0.69 | 308 | 27, 29 |

170.0 | 1.00 | 228 | 17, 19 |

165.0 | 1.20 | 188 | 11, 13, 24 |

156.7 | 1.20 | 188 | 7, 16, 23 |

137.5 | 2.73 | 128 | 8, 13 |

137.5 | 1.00 | 228 | 21, 13, 34 |

137.5 | 0.40 | 388 | 21, 34, 55 |

96.7 | 0.75 | 288 | 15, 26 |

69.0 | 0.98 | 288 | 21, 26, 5 |

66.7 | 0.96 | 288 | 11, 16, 27 |

37.3 | 0.84 | 288 | 10, 19 |

26.7 | 0.98 | 288 | 14, 13, 27 |

Parastichies are those criss-crossing lines that appear on sunflower heads, pinecones and pineapples as a result of how these plants grow. The numbers of these lines curving in different directions vary, but they tend to be Fibonacci numbers.

The phyllotactic spirals of sunflowers and other plants all have a divergence angle of 137.5° (the golden angle), but what happens with spirals based on other angles? As it turns out, you can produce parastichies with many different angles, but only the golden angle makes spirals for which all the parastichy numbers are Fibonacci numbers (in green above)!

Use the +/- buttons (or the A/Z, S/X and D/C keys) to change the variables of the spiral above and explore this for yourself.

Amazing things happen when you spin these spirals under a stroboscope... Check out some examples in this online zoetrope!