CPSC120A
Fundamentals of Computer Science I

Lab 12

Scope

Practice 1

Write a function called equilateral_area(edge_length) that computes the area of an equilateral triangle with the specified edge length.

\[area = \frac{\sqrt{3}}{4} \times length ^ 2 \] 








  
Practice 2




  Copy and paste your solution to the previous exercise into this one,
  and use it when writing a function
  called sierpinski_area(edge_length) that computes the
  area of a Sierpinski triangle of order one.  A Sierpinski Triangle of
  order one is an equilateral triangle with a triangular hole.  The
  vertices of the hole triangle are the mid points of the Sierpinski
  triangle's edges.  For example:




  




  


  

  

    
  

  





Trees



  When working with functions, abstraction is key.  You will soon find
  yourself in a position where you start thinking about problems in
  functions.  Being able to break a complex problem, like an advanced
  drawing, into smaller and simpler problems which can be solved with
  a function can make your code a lot easier to write, and a lot
  easier to read.



Details



  Create a function draw_tree(pen, x_location, y_location,
  width) in a file called forest.py. This function
  should take as a parameter a turtle object (pen) which can
  be used to draw a tree to the turtle window.  The base of the tree
  should be centered around the point \((x\_location, y\_location)\) and
  the largest set of branches should have a width as
  specified.  Your tree should look like the tree in the picture in
  the example below.




  Notice that a tree is defined by a brown square, and four green
  triangles which overlap each other.  For this, define two additional
  functions in the same file.  The first should be called
  draw_square(pen, x_location, y_location, side_length)
  which draws a filled in brown square square centered around the
  specified point.  The second should be
  called
  draw_triangle(pen, x_location, y_location, side_length),
  which creates an equilateral triangle with the specified side length
  centered around the specified point.




  It should also be noted that each triangle is \(10\%\) smaller than
  the triangle below.




  Test your function by calling the function multiple times with
  different parameters.  Make sure your code follows the course's code
  conventions.



Example Output

Turtle Drawing of a Tree




Hint



  
  

    
    
      
      
      
      
      
      
      
      

      
  • 
	You have already written code that draws an equilateral
	triangle in a post lab.  Look back at that code for help
	writing the draw_triangle function.
      
    • 

      
  • 
	Your draw_tree function should consist basically
	of one call to draw_square and four calls
	to draw_triangle.  You can use a for loop to make
	drawing the four triangles easier.
      
    • 

      
  • 
	You can use variable reassignment to keep track of
	the width of the next triangle to be drawn.  If at loop
	iteration 0 your width was 100, you want the width of the
	next triangle to be 90 at loop iteration 1.  You can compute
	this by multiplying 
	the current width by .9, and assigning the value back into
	your variable storing current width.
      
    • 
    

  






  
Challenge

  

    Using a for loop, draw a full forest of trees.  You should use a
    for loop to draw the following collection of trees.
  

Turtle Drawing of a Forest





Submission


Please show your source code and run your programs for the instructor or lab assistant. Only a programs that have perfect style and flawless functionality will be accepted as complete.