Script: Pythagoras tree
- Author:
- Juan Carlos Ponce Campuzano
- Topic:
- Fractal Geometry
Script
#=====================
# Define auxiliar tool
#=====================
A =(0, 0)
B = (4, 0)
base = Polygon(A, B, 4)
E = Midpoint(C, D)
arc = Semicircle(D, C)
F = Point(arc)
α = Angle(C, E, F)
C' = Rotate(C, α, E)
C'_1 = Rotate(C, α, E)
pointsBase = {D, C', C'_1, C}
ShowExtra = false
SetConditionToShowObject(A, ShowExtra)
SetConditionToShowObject(B, ShowExtra)
#SetConditionToShowObject(base, ShowExtra)
SetConditionToShowObject(C, ShowExtra)
SetConditionToShowObject(D, ShowExtra)
SetConditionToShowObject(E, ShowExtra)
SetConditionToShowObject(arc, ShowExtra)
#SetConditionToShowObject(F, ShowExtra)
SetConditionToShowObject(α, ShowExtra)
SetConditionToShowObject(C', ShowExtra)
SetConditionToShowObject(C'_1, ShowExtra)
SetConditionToShowObject(pointsBase, ShowExtra)
# In this case I defined the tool as:
# BasePoints( , , )
#=====================
# Construction begins
#=====================
N = 7
M = Slider(1, N, 1, 1, 160, false, true, false, false)
SetValue(M, N)
Lm = Sequence(1, M)
LN = Sequence(1, N)
Sname = Zip("S" + Text(n), n, LN)
Execute(Zip(name " = Sequence(k, k, 1, 2^("+(n+1)+"), 2)", name, Sname, n, LN ))
LK = Remove(LN, {1})
Tname = Zip("T" + Text(n), n, LK)
Execute(Zip(name " = Sequence(k, k, 1, 2^("+(n+1)+"), 4)", name, Tname, n, LK ))
#=====================
# Points
#=====================
Execute( Join( {"points1 = BasePoints(A, B, α)"}, Zip( "points"+(n+1)+" = Join(Zip(BasePoints(Element(points"+(n)+", k), Element(points"+(n)+", k + 1), α), k, S"+n+")) ", n, LN) ) )
SetVisibleInView(points8, 1, false)
#=====================
# Squares
#=====================
Execute(Zip( "squares"+n+" = Zip(Polygon(Element(points"+n+", k), Element(points"+n+", k + 1), 4), k, S"+n+")", n, LN))
#=====================
# Triangles
#=====================
triangles1 = Polygon(points1)
Execute( Zip( "triangles"+(n)+" = Zip(Polygon(Element(points"+(n)+", k), Element(points"+(n)+", k + 1), Element(points"+(n)+", k + 3)), k, T"+(n)+")", n, LK) )
#=========================
# Settings. Let's make it pretty :-)
#=========================
SetVisibleInView(Sname, 1, false)
SetVisibleInView(Tname, 1, false)
Execute(Zip("SetVisibleInView(S"+k+", 1, false)", k, LN))
Execute(Zip("SetVisibleInView(T"+k+", 1, false)", k, LK))
Execute(Zip("SetConditionToShowObject(points"+k+", "+k+"<=M)", k, LN))
Execute(Zip("SetConditionToShowObject(squares"+k+", "+k+"<=M)", k, LN))
Execute(Zip("SetConditionToShowObject(triangles"+k+", "+k+"<=M)", k, LN))
#====================================================
# Maybe there is an easier way to do this.
# What do you think Thijs?
# See this thread for details
#====================================================