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Mathematical Recreations
Acheron 2.0: a simple explorer of geometrical fractals

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.

A. Von Koch SnowFlakes
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)

B. Mandelbrot Curve
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)

C. Hilbert Curve
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)

D. Cesaro Curve
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)

E. Minkowski Sausage
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)

F. Sierpinski Curve
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)

G. Sierpinski Objects
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)

H. Peano Curve
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)

I. Squares Curve
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)

H. Heighway Dragon
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)



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