Question 1

In a grammar, the ____ is the starting point.

Accepted Answer

A)  base case 
B)  symbol 
C)  axiom 
D)  curve 
A)  base case 
B)  symbol 
C)  axiom 
D)  curve C

Question 2

Describe the two-step process that one should use to design well-formed recursive functions.

Accepted Answer

1. Are we done yet? Have we found a problem that is small enough to solve trivially? If so, solve it without any further work and return the answer.
2. If not, simplify the problem and solve the simpler problem. Combine the result of solving the simplified problem with what you know to solve the original. Return the combined result.

Question 3

Match each definition with its phrase.
-A construct that explains how to replace a symbol in a grammar with another symbol.

Accepted Answer

A)  Axiom 
B)  Production rule 
C)  L-system 
D)  Koch curve 
A)  Axiom 
B)  Production rule 
C)  L-system 
D)  Koch curve B

Question 4

Match each definition with its phrase.
-The starting point for a grammar.

Accepted Answer

A)  Axiom 
B)  Production rule 
C)  L-system 
D)  Koch curve 
A)  Axiom 
B)  Production rule 
C)  L-system 
D)  Koch curve

Question 5

In computer science terms, what is a grammar?

Accepted Answer

As it turns out, L-systems are based on

Question 6

Describe the Sierpinski triangle.

Accepted Answer

Assume that you have three triangles tha

Question 7

Describe how you could implement a recursive function to draw a Sierpinski triangle.

Accepted Answer

We would invent a simple base case calle

Question 8

Case Study 4:
1. Draw a trunk that is n units long.
2. Turn to the right 30 degrees and draw another tree with a trunk that is n − 15 units long.
3. Turn to the left 60 degrees and draw another tree with a trunk that is n − 15 units long.
-Refer to the instructions in the accompanying Case Study 4. How would you identify the base case?

Accepted Answer

When drawing a tree, the base case is a

Question 9

When drawing a tree with a recursive function, what is the base case?

Accepted Answer

A)  The trunk is less than some predefined number. 
B)  The number of branches is 20. 
C)  The condition becomes true. 
D)  The Python interpreter crashes. 
A)  The trunk is less than some predefined number. 
B)  The number of branches is 20. 
C)  The condition becomes true. 
D)  The Python interpreter crashes.

Question 10

What do the characters "[" and "]" represent in the L-systems grammar?

Accepted Answer

A)  Perform the operations between the surrounding elements first. 
B)  Save and restore the state. 
C)  Exit the program. 
D)  Invoke recursion. 
A)  Perform the operations between the surrounding elements first. 
B)  Save and restore the state. 
C)  Exit the program. 
D)  Invoke recursion.

Question 11

Writing a program to draw the Sierpinski triangle is more complex than the fractal tree, although it is still surprisingly simple.

Accepted Answer

A) True 
 B)False

Question 12

When drawing a Koch snowflake, what is the simplest possible curve?

Accepted Answer

A)  A straight line 
B)  A circle 
C)  A triangle 
D)  A square 
A)  A straight line 
B)  A circle 
C)  A triangle 
D)  A square

Question 13

Recursion can be used to express mathematical functions in an elegant way.

Accepted Answer

A) True 
 B)False

Question 14

In computer science, a grammar consists of:

Accepted Answer

A)  L-systems and Koch curves. 
B)  symbols and production rules. 
C)  base cases and recursive steps. 
D)  symbols and operations. 
A)  L-systems and Koch curves. 
B)  symbols and production rules. 
C)  base cases and recursive steps. 
D)  symbols and operations.

Question 15

What is the best description of the following function? 1. def hello ():
2) print("Hello World")
3) hello ()

Accepted Answer

A)  It is a simple and correctly implemented recursive function. 
B)  It is an erroneous illustration of a recursive function. 
C)  It is a recursive function that will only execute once. 
D)  It is a recursive function that will execute exactly 10 times. 
A)  It is a simple and correctly implemented recursive function. 
B)  It is an erroneous illustration of a recursive function. 
C)  It is a recursive function that will only execute once. 
D)  It is a recursive function that will execute exactly 10 times.

Question 16

In a recursive function, the ____ identifies when to stop.

Accepted Answer

A)  recursive square 
B)  erroneous step 
C)  recursive step 
D)  base case 
A)  recursive square 
B)  erroneous step 
C)  recursive step 
D)  base case

Question 17

Case Study 1:
1. def drawSquare(aTurtle, side):
2. for i in range(4):
3. aTurtle.forward(side)
4. aTurtle.right(90)
5.
6. def nestedBox(aTurtle, side):
7. if side >= 1:
8. drawSquare(aTurtle, side)
9. nestedBox(aTurtle, side - 5)
-Refer to the session in the accompanying Case Study 1. Line ____ represents the recursive step.

Accepted Answer

A)  2 
B)  7 
C)  8 
D)  9 
A)  2 
B)  7 
C)  8 
D)  9

Question 18

How is the Sierpinski triangle drawn?

Accepted Answer

A)  The largest triangle is completely drawn first. 
B)  Half of the largest triangle is drawn first, and the other half is drawn at the end. 
C)  All of the smallest triangles are drawn before any part of the larger ones. 
D)  The larger triangle is drawn in thirds. 
A)  The largest triangle is completely drawn first. 
B)  Half of the largest triangle is drawn first, and the other half is drawn at the end. 
C)  All of the smallest triangles are drawn before any part of the larger ones. 
D)  The larger triangle is drawn in thirds.

Question 19

A fractal tree requires only one recursive call.

Accepted Answer

A) True 
 B)False

Question 20

Every recursive program must have a base case in order to know when to stop.

Accepted Answer

A) True 
 B)False

In a grammar, the ____ is the starting point.

Describe the two-step process that one should use to design well-formed recursive functions.

Match each definition with its phrase. -A construct that explains how to replace a symbol in a grammar with another symbol.

Match each definition with its phrase. -The starting point for a grammar.

In computer science terms, what is a grammar?

Describe the Sierpinski triangle.

Describe how you could implement a recursive function to draw a Sierpinski triangle.

When drawing a tree with a recursive function, what is the base case?

What do the characters "[" and "]" represent in the L-systems grammar?

Writing a program to draw the Sierpinski triangle is more complex than the fractal tree, although it is still surprisingly simple.

When drawing a Koch snowflake, what is the simplest possible curve?

Recursion can be used to express mathematical functions in an elegant way.

In computer science, a grammar consists of:

What is the best description of the following function? 1. def hello (): 2) print("Hello World") 3) hello ()

In a recursive function, the ____ identifies when to stop.

How is the Sierpinski triangle drawn?

A fractal tree requires only one recursive call.

Every recursive program must have a base case in order to know when to stop.

Introduction to Python: Introduction to Numeric Types, Turtle Graphics, Simple for Loops and Functions

Pthon: Estimating PI: Math and Random Methods, Selection and Boolean Expressions, the Print Function

Codes and Other Secrets: String Operators and Methods, the Len Built-In Function, Keyword Parameters, User Input

Introducing the Python Collections: Lists, Dictionaries, Tuples, and Statistics

Bigger Data: File Io: the While Loop, String Formatting, Reading Online Data in CSV and Json Formats

Image Processing: Nested for Loops, Functions As Parameters, Namespaces, Lists of Lists

Data Mining: Cluster Analysis: More on the While Loop; Parrallel Lists

Cryptanalysis: Advanced Dictionaries and Lists, Regular Expressions

Astronomy: Creating Classes, Writing Constructors, Accessors, Mutators and Special Methods

Simulation:computer Simulation Using Objects

Father Was a Rectangle: Inheritance and Object-Oriented Design

Video Games: Multithreading, Event Handlers, Static Variables

Filters

Exam 9: Fractals: the Geometry of Nature: Recursion, Grammars and Production Rules

In a grammar, the ____ is the starting point.

Describe the two-step process that one should use to design well-formed recursive functions.

Match each definition with its phrase. -A construct that explains how to replace a symbol in a grammar with another symbol.

Match each definition with its phrase. -The starting point for a grammar.

In computer science terms, what is a grammar?

Describe the Sierpinski triangle.

Describe how you could implement a recursive function to draw a Sierpinski triangle.

When drawing a tree with a recursive function, what is the base case?

What do the characters "[" and "]" represent in the L-systems grammar?

Writing a program to draw the Sierpinski triangle is more complex than the fractal tree, although it is still surprisingly simple.

When drawing a Koch snowflake, what is the simplest possible curve?

Recursion can be used to express mathematical functions in an elegant way.

In computer science, a grammar consists of:

What is the best description of the following function? 1. def hello (): 2) print("Hello World") 3) hello ()

In a recursive function, the ____ identifies when to stop.

How is the Sierpinski triangle drawn?

A fractal tree requires only one recursive call.

Every recursive program must have a base case in order to know when to stop.

Introduction to Python: Introduction to Numeric Types, Turtle Graphics, Simple for Loops and Functions

Pthon: Estimating PI: Math and Random Methods, Selection and Boolean Expressions, the Print Function

Codes and Other Secrets: String Operators and Methods, the Len Built-In Function, Keyword Parameters, User Input

Introducing the Python Collections: Lists, Dictionaries, Tuples, and Statistics

Bigger Data: File Io: the While Loop, String Formatting, Reading Online Data in CSV and Json Formats

Image Processing: Nested for Loops, Functions As Parameters, Namespaces, Lists of Lists

Data Mining: Cluster Analysis: More on the While Loop; Parrallel Lists

Cryptanalysis: Advanced Dictionaries and Lists, Regular Expressions

Astronomy: Creating Classes, Writing Constructors, Accessors, Mutators and Special Methods

Simulation:computer Simulation Using Objects

Father Was a Rectangle: Inheritance and Object-Oriented Design

Video Games: Multithreading, Event Handlers, Static Variables

Filters