Programming Snazzy Fractals

1
Programming Snazzy Fractals

• Roshanak Roshandel Adair Dingle
• Department of Computer Science
• and Software Engineering
• Seattle University

2
Euclidean Geometry

• Triangles

• Circles

• Squares

• Rectangles

• Trapezoids

• Pentagons

• Hexagons

• Octagons

• Cylinders

3
Can we describe nature using Euclidean Geometry?

• Tree using cylinders??
• Mountains using triangles??
• Clouds using circles??
• Leaves??
• Rocks??

4
Well

• We can describe man made structures using
  Euclidean geometry
• But nature is full of rough edges and non uniform
  shapes
• Geometry of irregular shapes, non-smooth edges,
  infinite details, and infinite length

5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
What is a Fractal?

• Geometric figures just like circles and
  rectangles, but they also have some special
  properties
• Structural self-similarity
• All over nature
• Flowers, trees, mountains, stalagmite, snow
  flakes,
• Fractals are objects that look the same
  regardless of the magnification

15
(No Transcript)
16
The Sierpinski Triangle

• Step 1 Draw an equilateral triangle with sides
  of 2 triangle lengths each. Connect the
  midpoints of each side.

How many shaded triangles?
How many equilateral triangles do you now have?
17
Step 2

• Draw another equilateral triangle with sides of 4
  triangle lengths each.
• Connect the midpoints of the sides and shade the
  triangle in the center as before.

How many shaded triangles now?
18
Step 3
How many shaded triangle now?
19
Step 4
How many shaded triangles Now? What if we keep
going?
20
The Koch Snowflake
First step
After 2 steps
21
After 3 steps
22
After n steps
23
The Koch snowflake is six of these put together
to form . . .
. . . a snowflake.
24
Notice that the perimeter of the Koch snowflake
is infinite . . .
. . . but that the area it bounds is finite
(sure enough, it is contained in the white
square).
25
Do you see a pattern?

• We have to do something over and over and over
  again
• Its hard!
• Its tedious!
• Can we get help?

26
What can computers do?

• Computers are really good at
• following instructions
• processing data you provide (names, numbers,
  etc.)
• making decisions according to rules you specify
• repeating, repeating, repeating and repeating
• Lets look at some examples from Python
  Programming Language

27
1) following instructions

• Load the software (the Python interpreter) that
  will obey your commands!
• Type 'python
• You will see the interpreter's prompt gtgtgt
• This prompt tells you that the interpreter is
  waiting for another command.

28
Try the Following

• gtgtgt print "hello"
• gtgtgt print "name" use your name
• gtgtgt myName "name"
• gtgtgt print "hello " myName

29
2) Processing Data You Provide

• Let's use the Python interpreter as a calculator
  to see how it processes numbers.
• gtgtgt38 4
• gtgtgt23428973 345/3

30
Calculations.

• gtgtgt x int(raw_input('Please enter an integer
  '))
• gtgtgt y int(raw_input('Please enter an integer
  '))
• gtgtgt x y
• gtgtgt x y

31
3) making decisions according to rules you specify

• gtgtgt myWord raw_input('Please input a word')
• gtgtgt if (myWord is myName)
• ... print "Hello, oh great master " myName
• ... else
• ... print myWord " is not recognized by my
  instructions"

32
4) Repeating Repeating Repeating

• gtgtgt for i in range(1, 10)
• ... print myName
• gtgtgt for i in range(1, 10)
• ... for j in range(1,5)
• ... print myName,
• ... print " is great!"

33
Loops

• gtgtgt for i in range(1, 10)
• ... print myName " is
• ... for j in range(1,5)
• ... print "great, ",
• ... print "great!"

34
Function

• Do we have to type everything all the time? Can
  we store some instructions to be used later on?
• gtgtgt def WordCompare(someWord)
• ... if (someWord is myName)
• ... print "Hello, oh great master " myName
• ... else
• ... print someWord " is not recognized by my
  instructions"

35
Now lets do some fractal programming!
36
Resources

• Download Python Interpreter
• http//www.python.org
• For this presentation go to
• http//fac-staff.seattleu.edu/roshanak/fractals
• Questions? Send us an email
• roshanak_at_seattleu.edu
• dingle_at_seattleu.edu