# Deterministic Chaos

## 6.N. Period-Doubling Scaling and the Feigenbaum Constant

Here are the first few superstable points. For example,

at s*_{0} the point x = 1/2 is a fixed point,

at s*_{1} the point x = 1/2 belongs to a 2-cycle,

at s*_{2} the point x = 1/2 belongs to a 4-cycle,

and so on.

Here are the first 14 numerical values.

s*_{0} |
= 2.000000000000000000 |

s*_{1} |
= 3.236067977499789696 |

s*_{2} |
= 3.498561699327701520 |

s*_{3} |
= 3.554643880189573995 |

s*_{4} |
= 3.566667594798299166 |

s*_{5} |
= 3.569243531637110338 |

s*_{6} |
= 3.569795293749944621 |

s*_{7} |
= 3.569913465422348515 |

s*_{8} |
= 3.569938774233305491 |

s*_{9} |
= 3.569944194608064931 |

s*_{10} |
= 3.569945355486468581 |

s*_{11} |
= 3.569945604111078447 |

s*_{12} |
= 3.569945657358856505 |

s*_{13} |
= 3.569945668762899979 |

s*_{14} |
= 3.569945671205296863 |

We observe the superstable points are getting closer and closer
together. In fact, the sequence of s*_{n} converges to the
Myerberg point, s*_{infinity}, the same
point to which the period-doubling s_{i} converge.

Return to Period-Doubling Scaling and the
Feigenbaum Constant.