Function Repository Resource:

MinkowskiSausageCurve

Source Notebook

Generate the Minkowski sausage curve

Contributed by: Sander Huisman

ResourceFunction["MinkowskiSausageCurve"][n]

generates the line segments of the Minkowski sausage curve with n iterations.

ResourceFunction["MinkowskiSausageCurve"][{p₁,p₂},n]

uses the line connecting the points p₁ and p₂ as the initial line.

ResourceFunction["MinkowskiSausageCurve"][{p₁,p₂,…,p_n},n]

uses the lines joining the points p_i.

Details

The following transformation is done with each line segment:

The first four iterations:

ResourceFunction["MinkowskiSausageCurve"][n] is equivalent to ResourceFunction["MinkowskiSausageCurve"][{{-1,0},{1,0}},n].

The syntax ResourceFunction["MinkowskiSausageCurve"][Line[{p₁,p₂,…,p_n}],n] is also supported.

Examples

Basic Examples (2)

Generate the Minkowski sausage curve for two iterations:

In[1]:=

Out[1]=

Generate the curve for four iterations and visualize the result:

In[2]:=

Out[2]=

Scope (1)

Start from a square:

In[3]:=

Out[3]=

Properties and Relations (2)

MinkowskiSausageCurve and KochCurve have identical first iterates:

In[4]:=

${Graphics[ResourceFunction["MinkowskiSausageCurve"][1]], Graphics[KochCurve[ 1, {{1, 0}, {1, 90 \[Degree]}, {1, -90 \[Degree]}, {2, -90 \[Degree]}, {1, 90 \[Degree]}, {1, 90 \[Degree]}, {1, -90 \[Degree]}}]]} // GraphicsRow$

Out[4]=

Succeeding iterates have different behavior:

In[5]:=

${Graphics[ResourceFunction["MinkowskiSausageCurve"][2]], Graphics[KochCurve[ 2, {{1, 0}, {1, 90 \[Degree]}, {1, -90 \[Degree]}, {2, -90 \[Degree]}, {1, 90 \[Degree]}, {1, 90 \[Degree]}, {1, -90 \[Degree]}}]]} // GraphicsRow$

Out[5]=

The number of elements grows exponentially:

In[6]:=

Out[6]=

Publisher

SHuisman

Version History

1.0.0 – 28 October 2021

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License

Wolfram Function Repository

MinkowskiSausageCurve

Details