Function Repository Resource:

IteratedAffinePlot

Plot polygons after iteratively applying a translation, scaling and rotation

Contributed by: Radhika Prasad

ResourceFunction["IteratedAffinePlot"][rules, init]

plots the polygon described by the points init, and the transformed shape after applying the transformation given by rules.

ResourceFunction["IteratedAffinePlot"][rules, init,iter]

plots the polygon described by the points init, and the transformed shape after applying the transformation given by rules, for the number of iterations specified by iter.

Details and Options

init is a list of coordinates describing the initial polygon.

rules is a list of the form {{{x₁,y₁},s₁,θ₁},…}, where {x_i,y_i} specifies the coordinates of the centroid of the transformed polygons, s_i specifies the scaling factors and θ_i specifies the rotation angles.

iter plots the transformed shapes for the number of iterations as given by iter. It is an optional argument, with the default value being 1. It can take any of the following forms:

all iterations through n

plot only the n^th iteration

{n₁,n₂}

plots iterations from n₁ through n₂

{n₁,n₂,dn}

plots iterations from n₁ through n₂ in steps of dn

ResourceFunction["IteratedAffinePlot"] accepts all options of Graphics, with the additional option "ShowMarker".

With the default "ShowMarker"→True, markers showing the orientation of the transformed polygons are shown.

Examples

Basic Examples (1)

Show a single iteration of a given set of transformation rules, along with the initial polygon:

In[1]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]$

Out[1]=

Scope (2)

Show 5 iterations of a set of transformation rules:

In[2]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, 5]$

Out[2]=

Show the fifth through tenth iterations:

In[3]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {5, 10}]$

Out[3]=

Show the fifth, seventh and ninth iterations:

In[4]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {5, 10, 2}]$

Out[4]=

Show only the fifth iteration:

In[5]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {{5}}]$

Out[5]=

Use Graphics options:

In[6]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, \[Pi]/6}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {{5}}, Background -> LightBlue, Frame -> True]$

Out[6]=

Options (1)

ShowMarker (1)

Set "ShowMarker"→False to omit the markers in the results:

In[7]:=

$ResourceFunction[ "IteratedAffinePlot"][{{{1/2, 1/2}, 0.85, 30 \[Degree]}, {{-.1, .5}, .35, 0}}, {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {5, 10, 2}, "ShowMarker" -> False]$