How to resolve the algorithm Pythagoras tree step by step in the PureBasic programming language

Published on 12 May 2024 09:40 PM
#Purebasic

How to resolve the algorithm Pythagoras tree step by step in the PureBasic programming language

Table of Contents

Problem Statement

The Pythagoras tree is a fractal tree constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to represent the Pythagorean theorem.

Construct a Pythagoras tree of order 7 using only vectors (no rotation or trigonometric functions).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pythagoras tree step by step in the PureBasic programming language

Source code in the purebasic programming language

EnableExplicit
DisableDebugger

Procedure.d maxXY(a.d,b.d,c.d,d.d)
  If a<b : Swap a,b : EndIf
  If a<c : Swap a,c : EndIf
  If a<d : Swap a,d : EndIf  
  ProcedureReturn a
EndProcedure

Procedure.d minXY(a.d,b.d,c.d,d.d)
  If a>b : Swap a,b : EndIf
  If a>c : Swap a,c : EndIf
  If a>d : Swap a,d : EndIf  
  ProcedureReturn a
EndProcedure

Procedure Ptree(x1.d, y1.d, x2.d, y2.d, d.i=0)
  If d>10 : ProcedureReturn : EndIf
  
  Define dx.d=x2-x1,
         dy.d=y1-y2,
         x3.d=x2-dy,
         y3.d=y2-dx,
         x4.d=x1-dy,
         y4.d=y1-dx,
         x5.d=x4+(dx-dy)/2.0,
         y5.d=y4-(dx+dy)/2.0,
         p1.d=(maxXY(x1,x2,x3,x4)+minXY(x1,x2,x3,x4))/2.0,
         p2.d=(maxXY(y1,y2,y3,y4)+minXY(y1,y2,y3,y4))/2.0,
         p3.d=(maxXY(x1,x2,x3,x4)-minXY(x1,x2,x3,x4))        
    
  FrontColor(RGB(Random(125,1),Random(255,125),Random(125,1)))    
  LineXY(x1,y1,x2,y2)
  LineXY(x2,y2,x3,y3)
  LineXY(x3,y3,x4,y4)
  LineXY(x4,y4,x1,y1)
  BoxedGradient(minXY(x1,x2,x3,x4),minXY(y1,y2,y3,y4),p3,p3)
  FillArea(p1,p2,-1)
  
  Ptree(x4,y4,x5,y5,d+1)
  Ptree(x5,y5,x3,y3,d+1)
  
EndProcedure

Define w1.i=800,
       h1.i=w1*11/16,
       w2.i=w1/2,
       di.i=w1/12

If OpenWindow(0,#PB_Ignore,#PB_Ignore,w1,h1,"Pythagoras tree")
  If CreateImage(0,w1,h1,24,0) And StartDrawing(ImageOutput(0))
    DrawingMode(#PB_2DDrawing_Gradient)
    BackColor($000000)
    Ptree(w2-di,h1-10,w2+di,h1-10)    
    StopDrawing()
  EndIf
  ImageGadget(0,0,0,0,0,ImageID(0))  
  Repeat : Until WaitWindowEvent(50)=#PB_Event_CloseWindow
EndIf
End

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