Mathematical Recreations

Acheron 2.0

Acheron 2.0 Overview

The left pane of Acheron 2.0 screen is used to select the fractal curve. The selection automatically displays the ribbon category related to the selected curve.

  1. Von Koch SnowFlakes

    2. Acheron 2.0 Ribbon - VonKoch

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 10
    • Frame:
      1. Line
      2. Triangle
      3. Square
      4. Pentagon
      5. Hexagon
    • Similarity Ratio: Ratio between Length of Segment and Height of Grain, expressed as 10th of percent (by default, 333, equivalent to 33 %). Ratio ranges from 150 to 1000.
    • Grain Orientation: Outside, Inside or Random
    • Grain: Triangle (Standard Von Koch curve) and Square
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  2. Mandelbrot Curve

    3. Acheron 2.0 Ribbon - Mandelbrot

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 10
    • Frame:
      1. Line
      2. Square
    • Grain: Normal (Standard Mandelbrot curve) and Clipped
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  3. Hilbert Curve

    4. Acheron 2.0 Ribbon - Hilbert

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 10
    • Similarity Ratio: from 1 to 12
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  4. Cesaro Curve

    5. Acheron 2.0 Ribbon - Cesaro

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 10
    • Similarity Ratio: from 1 to 12
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  5. Minkowski Sausage

    6. Acheron 2.0 Ribbon - Minkowski

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 10
    • Frame:
      1. Line
      2. Triangle
      3. Square
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  6. Sierpinski Curve

    7. Acheron 2.0 Ribbon - Sierpinski

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 8
    • Grain:
      1. Normal
      2. Square
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  7. Sierpinski Objects

    8. Acheron 2.0 Ribbon - Sierpinski Objects

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 8
    • Frame:
      1. Triangle
      2. Square
      3. Pentagon
      4. Hexagon
    • Grain:
      1. Normal
      2. Filled
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  8. Peano Curve

    9. Acheron 2.0 Ribbon - Peano

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 5
    • Grain:
      1. Normal
      2. Filled
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  9. Squares Curve

    10. Acheron 2.0 Ribbon - Squares

    The following settings are available to modify the rendering of the fractals.
    • Recursion Level: from 1 to 5
    • Grain:
      1. Normal
      2. Filled
      3. Outlined
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)

  10. Heighway Dragon

    11. Acheron 2.0 Ribbon - Heighway Dragon

    The following settings are available to modify the rendering of the fractals.
    • Folding Code: a succession of up to 16 characters 0 and 1 that code for paper folding
    • Display Settings: Curve Colour, Background Start and End Colour, Background Fading (7 different types)