Strings Revisited

Throughout the first chapters of this book we have used strings to represent words or phrases that we wanted to print out. Our definition was simple: a string is simply some characters inside quotes. In this chapter we explore strings in much more detail.

A Collection Data Type

So far we have seen built-in types like: int, float, bool, str and we’ve seen lists. int, float, and bool are considered to be simple or primitive data types because their values are not composed of any smaller parts. They cannot be broken down. On the other hand, strings and lists are different from the others because they are made up of smaller pieces. In the case of strings, they are made up of smaller strings each containing one character.

Types that are comprised of smaller pieces are called collection data types. Depending on what we are doing, we may want to treat a collection data type as a single entity (the whole), or we may want to access its parts. This ambiguity is useful.

Strings can be defined as sequential collections of characters. This means that the individual characters that make up the string are assumed to be in a particular order from left to right.

A string that contains no characters, often referred to as the empty string, is still considered to be a string. It is simply a sequence of zero characters and is represented by ‘’ or “” (two single or two double quotes with nothing in between).

Operations on Strings

In general, you cannot perform mathematical operations on strings, even if the strings look like numbers. The following are illegal (assuming that message has type string):

message - 1
"Hello" / 123
message * "Hello"
"15" + 2

Interestingly, the + operator does work with strings, but for strings, the + operator represents concatenation, not addition. Concatenation means joining the two operands by linking them end-to-end. For example:


The output of this program is banana nut bread. The space before the word nut is part of the string and is necessary to produce the space between the concatenated strings. Take out the space and run it again.

The * operator also works on strings. It performs repetition. For example, 'Fun'*3 is 'FunFunFun'. One of the operands has to be a string and the other has to be an integer.


This interpretation of + and * makes sense by analogy with addition and multiplication. Just as 4*3 is equivalent to 4+4+4, we expect "Go"*3 to be the same as "Go"+"Go"+"Go", and it is. Note also in the last example that the order of operations for * and + is the same as it was for arithmetic. The repetition is done before the concatenation. If you want to cause the concatenation to be done first, you will need to use parenthesis.

Check your understanding

str-1: What is printed by the following statements?

s = "python"
t = "rocks"

str-2: What is printed by the following statements?

s = "python"
excl = "!"

Index Operator: Working with the Characters of a String

The indexing operator (Python uses square brackets to enclose the index) selects a single character from a string. The characters are accessed by their position or index value. For example, in the string shown below, the 14 characters are indexed left to right from postion 0 to position 13.

index values

It is also the case that the positions are named from right to left using negative numbers where -1 is the rightmost index and so on. Note that the character at index 6 (or -8) is the blank character.


The expression school[2] selects the character at index 2 from school, and creates a new string containing just this one character. The variable m refers to the result.

Remember that computer scientists often start counting from zero. The letter at index zero of "Luther College" is L. So at position [2] we have the letter t.

If you want the zero-eth letter of a string, you just put 0, or any expression with the value 0, in the brackets. Give it a try.

The expression in brackets is called an index. An index specifies a member of an ordered collection. In this case the collection of characters in the string. The index indicates which character you want. It can be any integer expression so long as it evaluates to a valid index value.

Note that indexing returns a string — Python has no special type for a single character. It is just a string of length 1.

Check your understanding

str-3: What is printed by the following statements?

s = "python rocks"

str-4: What is printed by the following statements?

s = "python rocks"
print(s[2] + s[-5])

String Methods

We previously saw that each turtle instance has its own attributes and a number of methods that can be applied to the instance. For example, we wrote tess.right(90) when we wanted the turtle object tess to perform the right method to turn to the right 90 degrees. The “dot notation” is the way we connect the name of an object to the name of a method it can perform.

Strings are also objects. Each string instance has its own attributes and methods. The most important attribute of the string is the collection of characters. There are a wide variety of methods. Try the following program.


In this example, upper is a method that can be invoked on any string object to create a new string in which all the characters are in uppercase. lower works in a similar fashion changing all characters in the string to lowercase. (The original string ss remains unchanged. A new string tt is created.)

In addition to upper and lower, the following table provides a summary of some other useful string methods. There are a few activecode examples that follow so that you can try them out.

Method Parameters Description
upper none Returns a string in all uppercase
lower none Returns a string in all lowercase
capitalize none Returns a string with first character capitalized, the rest lower
strip none Returns a string with the leading and trailing whitespace removed
lstrip none Returns a string with the leading whitespace removed
rstrip none Returns a string with the trailing whitespace removed
count item Returns the number of occurrences of item
replace old, new Replaces all occurrences of old substring with new
center width Returns a string centered in a field of width spaces
ljust width Returns a string left justified in a field of width spaces
rjust width Returns a string right justified in a field of width spaces
find item Returns the leftmost index where the substring item is found
rfind item Returns the rightmost index where the substring item is found
index item Like find except causes a runtime error if item is not found
rindex item Like rfind except causes a runtime error if item is not found

You should experiment with these methods so that you understand what they do. Note once again that the methods that return strings do not change the original. You can also consult the Python documentation for strings.



Check your understanding

str-5: What is printed by the following statements?

s = "python rocks"
print(s.count("o") + s.count("p"))

str-6: What is printed by the following statements?

s = "python rocks"


The len function, when applied to a string, returns the number of characters in a string.


To get the last letter of a string, you might be tempted to try something like this:


That won’t work. It causes the runtime error IndexError: string index out of range. The reason is that there is no letter at index position 6 in "Banana". Since we started counting at zero, the six indexes are numbered 0 to 5. To get the last character, we have to subtract 1 from length. Give it a try in the example above.


Typically, a Python programmer will access the last character by combining the two lines of code from above.

lastch = fruit[len(fruit)-1]

Check your understanding

str-7: What is printed by the following statements?

s = "python rocks"

str-8: What is printed by the following statements?

s = "python rocks"

The Slice Operator

A substring of a string is called a slice. Selecting a slice is similar to selecting a character:


The slice operator [n:m] returns the part of the string from the n’th character to the m’th character, including the first but excluding the last. In other words, start with the character at index n and go up to but do not include the character at index m. This behavior may seem counter-intuitive but if you recall the range function, it did not include its end point either.

If you omit the first index (before the colon), the slice starts at the beginning of the string. If you omit the second index, the slice goes to the end of the string.


What do you think fruit[:] means?

Check your understanding

str-9: What is printed by the following statements?

s = "python rocks"

str-10: What is printed by the following statements?

s = "python rocks"


This workspace is provided for your convenience. You can use this activecode window to try out anything you like.


String Comparison

The comparison operators also work on strings. To see if two strings are equal you simply write a boolean expression using the equality operator.


Other comparison operations are useful for putting words in lexicographical order. This is similar to the alphabetical order you would use with a dictionary, except that all the uppercase letters come before all the lowercase letters.


It is probably clear to you that the word apple would be less than (come before) the word banana. After all, a is before b in the alphabet. But what if we consider the words apple and Apple? Are they the same?


It turns out, as you recall from our discussion of variable names, that uppercase and lowercase letters are considered to be different from one another. The way the computer knows they are different is that each character is assigned a unique integer value. “A” is 65, “B” is 66, and “5” is 53. The way you can find out the so called ordinal value for a given character is to use a character function called ord.


When you compare characters or strings to one another, Python converts the characters into their equivalent ordinal values and compares the integers from left to right. As you can see from the example above, “a” is greater than “A” so “apple” is greater than “Apple”.

Humans commonly ignore capitalization when comparing two words. However, computers do not. A common way to address this issue is to convert strings to a standard format, such as all lowercase, before performing the comparison.

There is also a similar function called chr that converts integers into their character equivalent.


One thing to note in the last two examples is the fact that the space character has an ordinal value (32). Even though you don’t see it, it is an actual character. We sometimes call it a nonprinting character.

Check your understanding

str-11: Evaluate the following comparison:

"Dog" < "Doghouse"

str-12: Evaluate the following comparison:

"dog" < "Dog"

str-13: Evaluate the following comparison:

"dog" < "Doghouse"

Strings are Immutable

One final thing that makes strings different from some other Python collection types is that you are not allowed to modify the individual characters in the collection. It is tempting to use the [] operator on the left side of an assignment, with the intention of changing a character in a string. For example, in the following code, we would like to change the first letter of greeting.


Instead of producing the output Jello, world!, this code produces the runtime error TypeError: 'str' object does not support item assignment.

Strings are immutable, which means you cannot change an existing string. The best you can do is create a new string that is a variation on the original.


The solution here is to concatenate a new first letter onto a slice of greeting. This operation has no effect on the original string.

Check your understanding

str-14: What is printed by the following statements:

s = "Ball"
s[0] = "C"

Traversal and the for Loop: By Item

A lot of computations involve processing a collection one item at a time. For strings this means that we would like to process one character at a time. Often we start at the beginning, select each character in turn, do something to it, and continue until the end. This pattern of processing is called a traversal.

We have previously seen that the for statement can iterate over the items of a sequence (a list of names in the case below).


Recall that the loop variable takes on each value in the sequence of names. The body is performed once for each name. The same was true for the sequence of integers created by the range function.


Since a string is simply a sequence of characters, the for loop iterates over each character automatically.


The loop variable achar is automatically reassigned each character in the string “Go Spot Go”. We will refer to this type of sequence iteration as iteration by item. Note that it is only possible to process the characters one at a time from left to right.

Check your understanding

str-15: How many times is the word HELLO printed by the following statements?

s = "python rocks"
for ch in s:

str-16: How many times is the word HELLO printed by the following statements?

s = "python rocks"
for ch in s[3:8]:

Traversal and the for Loop: By Index

It is also possible to use the range function to systematically generate the indices of the characters. The for loop can then be used to iterate over these positions. These positions can be used together with the indexing operator to access the individual characters in the string.

Consider the following codelens example.


The index positions in “apple” are 0,1,2,3 and 4. This is exactly the same sequence of integers returned by range(5). The first time through the for loop, idx will be 0 and the “a” will be printed. Then, idx will be reassigned to 1 and “p” will be displayed. This will repeat for all the range values up to but not including 5. Since “e” has index 4, this will be exactly right to show all of the characters.

In order to make the iteration more general, we can use the len function to provide the bound for range. This is a very common pattern for traversing any sequence by position. Make sure you understand why the range function behaves correctly when using len of the string as its parameter value.


You may also note that iteration by position allows the programmer to control the direction of the traversal by changing the sequence of index values. Recall that we can create ranges that count down as well as up so the following code will print the characters from right to left.


Trace the values of idx and satisfy yourself that they are correct. In particular, note the start and end of the range.

Check your understanding

str-17: How many times is the letter o printed by the following statements?

s = "python rocks"
for idx in range(len(s)):
   if idx % 2 == 0:

Traversal and the while Loop

The while loop can also control the generation of the index values. Remember that the programmer is responsible for setting up the initial condition, making sure that the condition is correct, and making sure that something changes inside the body to guarantee that the condition will eventually fail.


The loop condition is position < len(fruit), so when position is equal to the length of the string, the condition is false, and the body of the loop is not executed. The last character accessed is the one with the index len(fruit)-1, which is the last character in the string.

Here is the same example in codelens so that you can trace the values of the variables.


Check your understanding

str-18: How many times is the letter o printed by the following statements?

s = "python rocks"
idx = 1
while idx < len(s):
   idx = idx + 2


This workspace is provided for your convenience. You can use this activecode window to try out anything you like.


The in and not in operators

The in operator tests if one string is a substring of another:


Note that a string is a substring of itself, and the empty string is a substring of any other string. (Also note that computer scientists like to think about these edge cases quite carefully!)


The not in operator returns the logical opposite result of in.


The Accumulator Pattern with Strings

Combining the in operator with string concatenation using + and the accumulator pattern, we can write a function that removes all the vowels from a string. The idea is to start with a string and iterate over each character, checking to see if the character is a vowel. As we process the characters, we will build up a new string consisting of only the nonvowel characters. To do this, we use the accumulator pattern.

Remember that the accumulator pattern allows us to keep a “running total”. With strings, we are not accumulating a numeric total. Instead we are accumulating characters onto a string.


Line 5 uses the not in operator to check whether the current character is not in the string vowels. The alternative to using this operator would be to write a very large if statement that checks each of the individual vowel characters. Note we would need to use logical and to be sure that the character is not any of the vowels.

if eachChar != 'a'  and eachChar != 'e'  and eachChar != 'i'  and
   eachChar != 'o'  and eachChar != 'u'  and eachChar != 'A'  and
   eachChar != 'E'  and eachChar != 'I'  and eachChar != 'O'  and
   eachChar != 'U':

     sWithoutVowels = sWithoutVowels + eachChar

Look carefully at line 6 in the above program (sWithoutVowels = sWithoutVowels + eachChar). We will do this for every character that is not a vowel. This should look very familiar. As we were describing earlier, it is an example of the accumulator pattern, this time using a string to “accumulate” the final result. In words it says that the new value of sWithoutVowels will be the old value of sWithoutVowels concatenated with the value of eachChar. We are building the result string character by character.

Take a close look also at the initialization of sWithoutVowels. We start with an empty string and then begin adding new characters to the end.

Step thru the function using codelens to see the accumulator variable grow.


Check your understanding

str-19: What is printed by the following statements:

s = "ball"
r = ""
for item in s:
   r = item.upper() + r


This workspace is provided for your convenience. You can use this activecode window to try out anything you like.


Turtles and Strings and L-Systems

This section describes a much more interested example of string iteration and the accumulator pattern. Even though it seems like we are doing something that is much more complex, the basic processing is the same as was shown in the previous sections.

In 1968 Astrid Lindenmayer, a biologist, invented a formal system that provides a mathematical description of plant growth known as an L-system. L-systems were designed to model the growth of biological systems. You can think of L-systems as containing the instructions for how a single cell can grow into a complex organism. L-systems can be used to specify the rules for all kinds of interesting patterns. In our case, we are going to use them to specify the rules for drawing pictures.

The rules of an L-system are really a set of instructions for transforming one string into a new string. After a number of these string transformations are complete, the string contains a set of instructions. Our plan is to let these instructions direct a turtle as it draws a picture.

To begin, we will look at an example set of rules:

A Axiom
A -> B Rule 1 Change A to B
B -> AB Rule 2 Change B to AB

Each rule set contains an axiom which represents the starting point in the transformations that will follow. The rules are of the form:

left hand side -> right hand side

where the left and side is a single symbol and the right had side is a sequence of symbols. You can think of both sides as being simple strings. The way the rules are used is to replace occurrences of the left hand side with the corresponding right hand side.

Now lets look at these simple rules in action, starting with the string A:

B      Apply Rule 1  (A is replaced by B)
AB     Apply Rule 2  (B is replaced by AB)
BAB    Apply Rule 1 to A then Rule 2 to B
ABBAB  Apply Rule 2 to B, Rule 1 to A, and Rule 2 to B

Notice that each line represents a new transformation for entire string. Each character that matches a left-hand side of a rule in the original has been replaced by the corresponding right-hand side of that same rule. After doing the replacement for each character in the original, we have one transformation.

So how would we encode these rules in a Python program? There are a couple of very important things to note here:

  1. Rules are very much like if statements.
  2. We are going to start with a string and iterate over each of its characters.
  3. As we apply the rules to one string we leave that string alone and create a brand new string using the accumulator pattern. When we are all done with the original we replace it with the new string.

Lets look at a simple Python program that implements the example set of rules described above.


Try running the example above with different values for the numIters parameter. You should see that for values 1, 2, 3, and 4, the strings generated follow the example above exactly.

One of the nice things about the program above is that if you want to implement a different set of rules, you don’t need to re-write the entire program. All you need to do is re-write the applyRules function.

Suppose you had the following rules:

A Axiom
A -> BAB Rule 1 Change A to BAB

What kind of a string would these rules create? Modify the program above to implement the rule.

Now lets look at a real L-system that implements a famous drawing. This L-system has just two rules:

F Axiom
F -> F-F++F-F Rule 1

This L-system uses symbols that will have special meaning when we use them later with the turtle to draw a picture.

F Go forward by some number of units
B Go backward by some number of units
- Turn left by some degrees
+ Turn right by some degrees

Here is the applyRules function for this L-system.

def applyRules(ch):
    newstr = ""
    if ch == 'F':
        newstr = 'F-F++F-F'   # Rule 1
        newstr = ch    # no rules apply so keep the character

    return newstr

Pretty simple so far. As you can imagine this string will get pretty long with a few applications of the rules. You might try to expand the string a couple of times on your own just to see.

The last step is to take the final string and turn it into a picture. Lets assume that we are always going to go forward or backward by 5 units. In addition we will also assume that when the turtle turns left or right we’ll turn by 60 degrees. Now look at the string F-F++F-F. You might try to us the explanation above to show the resulting picture that this simple string represents. At this point its not a very exciting drawing, but once we expand it a few times it will get a lot more interesting.

To create a Python function to draw a string we will write a function called drawLsystem The function will take four parameters:

  • A turtle to do the drawing
  • An expanded string that contains the results of expanding the rules above.
  • An angle to turn
  • A distance to move forward or backward
def drawLsystem(aTurtle,instructions,angle,distance):
    for cmd in instructions:
        if cmd == 'F':
        elif cmd == 'B':
        elif cmd == '+':
        elif cmd == '-':
            print('Error:', cmd, 'is an unknown command')

Here is the complete program in activecode. The main function first creates the L-system string and then it creates a turtle and passes it and the string to the drawing function.


Feel free to try some different angles and segment lengths to see how the drawing changes.

Looping and counting

We will finish this chapter with a few more examples that show variations on the theme of iteration through the characters of a string. We will implement a few of the methods that we described earlier to show how they can be done.

The following program counts the number of times a particular letter, aChar, appears in a string. It is another example of the accumulator pattern that we have seen in previous chapters.


The function count takes a string as its parameter. The for statement iterates through each character in the string and checks to see if the character is equal to the value of aChar. If so, the counting variable, lettercount, is incremented by one. When all characters have been processed, the lettercount is returned.

A find function

Here is an implementation for the find method.


In a sense, find is the opposite of the indexing operator. Instead of taking an index and extracting the corresponding character, it takes a character and finds the index where that character appears for the first time. If the character is not found, the function returns -1.

The while loop in this example uses a slightly more complex condition than we have seen in previous programs. Here there are two parts to the condition. We want to keep going if there are more characters to look through and we want to keep going if we have not found what we are looking for. The variable found is a boolean variable that keeps track of whether we have found the character we are searching for. It is initialized to False. If we find the character, we reassign found to True.

The other part of the condition is the same as we used previously to traverse the characters of the string. Since we have now combined these two parts with a logical and, it is necessary for them both to be True to continue iterating. If one part fails, the condition fails and the iteration stops.

When the iteration stops, we simply ask a question to find out why and then return the proper value.


This pattern of computation is sometimes called a eureka traversal because as soon as we find what we are looking for, we can cry Eureka! and stop looking. The way we stop looking is by setting found to True which causes the condition to fail.

Optional parameters

To find the locations of the second or third occurrence of a character in a string, we can modify the find function, adding a third parameter for the starting position in the search string:


The call find2('banana', 'a', 2) now returns 3, the index of the first occurrence of ‘a’ in ‘banana’ after index 2. What does find2('banana', 'n', 3) return? If you said, 4, there is a good chance you understand how find2 works. Try it.

Better still, we can combine find and find2 using an optional parameter.


The call find3('banana', 'a', 2) to this version of find behaves just like find2, while in the call find3('banana', 'a'), start will be set to the default value of 0.

Adding another optional parameter to find makes it search from a starting position, up to but not including the end position.


The optional value for end is interesting. We give it a default value None if the caller does not supply any argument. In the body of the function we test what end is and if the caller did not supply any argument, we reassign end to be the length of the string. If the caller has supplied an argument for end, however, the caller’s value will be used in the loop.

The semantics of start and end in this function are precisely the same as they are in the range function.

Character classification

It is often helpful to examine a character and test whether it is upper- or lowercase, or whether it is a character or a digit. The string module provides several constants that are useful for these purposes. One of these, string.digits is equivalent to “0123456789”. It can be used to check if a character is a digit using the in operator.

The string string.ascii_lowercase contains all of the ascii letters that the system considers to be lowercase. Similarly, string.ascii_uppercase contains all of the uppercase letters. string.punctuation comprises all the characters considered to be punctuation. Try the following and see what you get.


For more information consult the string module documentaiton (see Global Module Index).


This workspace is provided for your convenience. You can use this activecode window to try out anything you like.



This chapter introduced a lot of new ideas. The following summary may prove helpful in remembering what you learned.

indexing ([])
Access a single character in a string using its position (starting from 0). Example: 'This'[2] evaluates to 'i'.
length function (len)
Returns the number of characters in a string. Example: len('happy') evaluates to 5.
for loop traversal (for)

Traversing a string means accessing each character in the string, one at a time. For example, the following for loop:

for ix in 'Example':

executes the body of the loop 7 times with different values of ix each time.

slicing ([:])
A slice is a substring of a string. Example: 'bananas and cream'[3:6] evaluates to ana (so does 'bananas and cream'[1:4]).
string comparison (>, <, >=, <=, ==, !=)
The six common comparision operators work with strings, evaluating according to lexigraphical order. Examples: 'apple' < 'banana' evaluates to True. 'Zeta' < 'Appricot' evaluates to False. 'Zebra' <= 'aardvark' evaluates to True because all upper case letters precede lower case letters.
in and not in operator (in, not in)
The in operator tests whether one string is contained inside another string. Examples: 'heck' in "I'll be checking for you." evaluates to True. 'cheese' in "I'll be checking for you." evaluates to False.


collection data type
A data type in which the values are made up of components, or elements, that are themselves values.
default value
The value given to an optional parameter if no argument for it is provided in the function call.
dot notation
Use of the dot operator, ., to access functions inside a module, or to access methods and attributes of an object.
A compound data type whose elements can not be assigned new values.
A variable or value used to select a member of an ordered collection, such as a character from a string, or an element from a list.
optional parameter
A parameter written in a function header with an assignment to a default value which it will receive if no corresponding argument is given for it in the function call.
A part of a string (substring) specified by a range of indices. More generally, a subsequence of any sequence type in Python can be created using the slice operator (sequence[start:stop]).
To iterate through the elements of a collection, performing a similar operation on each.
Any of the characters that move the cursor without printing visible characters. The constant string.whitespace contains all the white-space characters.


  1. What is the result of each of the following:

    1. ‘Python’[1]
    2. “Strings are sequences of characters.”[5]
    3. len(“wonderful”)
    4. ‘Mystery’[:4]
    5. ‘p’ in ‘Pineapple’
    6. ‘apple’ in ‘Pineapple’
    7. ‘pear’ not in ‘Pineapple’
    8. ‘apple’ > ‘pineapple’
    9. ‘pineapple’ < ‘Peach’
    1. ‘Python’[1] = ‘y’
    2. ‘Strings are sequences of characters.’[5] = ‘g’
    3. len(‘wonderful’) = 9
    4. ‘Mystery’[:4] = ‘Myst’
    5. ‘p’ in ‘Pineapple’ = True
    6. ‘apple’ in ‘Pineapple’ = True
    7. ‘pear’ not in ‘Pineapple’ = True
    8. ‘apple’ > ‘pineapple’ = False
    9. ‘pineapple’ < ‘Peach’ = False
    Show Comments
  2. In Robert McCloskey’s book Make Way for Ducklings, the names of the ducklings are Jack, Kack, Lack, Mack, Nack, Ouack, Pack, and Quack. This loop tries to output these names in order.

    prefixes = "JKLMNOPQ"
        suffix = "ack"
        for p in prefixes:
            print(p + suffix)

    Of course, that’s not quite right because Ouack and Quack are misspelled. Can you fix it?


  3. Assign to a variable in your program a triple-quoted string that contains your favorite paragraph of text - perhaps a poem, a speech, instructions to bake a cake, some inspirational verses, etc.

    Write a function that counts the number of alphabetic characters (a thru z, or A thru Z) in your text and then keeps track of how many are the letter ‘e’. Your function should print an analysis of the text like this:

    Your text contains 243 alphabetic characters, of which 109 (44.8%) are 'e'.




    Show Comments
  4. Print out a neatly formatted multiplication table, up to 12 x 12.


  5. Write a function that will return the number of digits in an integer.




    Show Comments
  6. Write a function that reverses its string argument.


  7. Write a function that mirrors its argument.




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  8. Write a function that removes all occurrences of a given letter from a string.


  9. Write a function that recognizes palindromes. (Hint: use your reverse function to make this easy!).




    Show Comments
  10. Write a function that counts how many times a substring occurs in a string.


  11. Write a function that removes the first occurrence of a string from another string.




    Show Comments
  12. Write a function that removes all occurrences of a string from another string.


  13. Here is another interesting L-System called a Hilbert curve. Use 90 degrees:

    L -> +RF-LFL-FR+
    R -> -LF+RFR+FL-




    Show Comments
  14. Here is a dragon curve. Use 90 degrees.:

    X -> X+YF+
    Y -> -FX-Y


  15. Here is something called an arrowhead curve. Use 60 degrees.:

    X -> YF+XF+Y
    Y -> XF-YF-X




    Show Comments
  16. Try the Peano-Gosper curve. Use 60 degrees.:

    X -> X+YF++YF-FX--FXFX-YF+
    Y -> -FX+YFYF++YF+FX--FX-Y


  17. The Sierpinski Triangle. Use 60 degrees.:

    F -> FF
    X -> --FXF++FXF++FXF--




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  18. Write a function that implements a substitution cipher. In a substitution cipher one letter is substituted for another to garble the message. For example A -> Q, B -> T, C -> G etc. your function should take two parameters, the message you want to encrypt, and a string that represents the mapping of the 26 letters in the alphabet. Your function should return a string that is the encrypted version of the message.


  19. Write a function that decrypts the message from the previous exercise. It should also take two parameters. The encrypted message, and the mixed up alphabet. The function should return a string that is the same as the original unencrypted message.




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  20. Write a function called removeDups that takes a string and creates a new string by only adding those characters that are not already present. In other words, there will never be a duplicate letter added to the new string.


  21. Write a function called rot13 that uses the Caesar cipher to encrypt a message. The Caesar cipher works like a substitution cipher but each character is replaced by the character 13 characters to ‘its right’ in the alphabet. So for example the letter a becomes the letter n. If a letter is past the middle of the alphabet then the counting wraps around to the letter a again, so n becomes a, o becomes b and so on. Hint: Whenever you talk about things wrapping around its a good idea to think of modulo arithmetic.




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