Problem 1: 5d100s

• Every week before we start playing, each person in my D&D group rolls 5 (virtual) 100-sided dice
  • A 100-sided dice has numbers 1-100 on its faces
• We like to use the sum of the 5 dice to predict how lucky or unlucky we’ll be that night
• But what would be exceptional?
• Your group’s task: Roll 5 100-sided dice 10,000 times. What is the maximum value you got?

Problem 2: Olympic Flags

• With the Olympics going on, you’ve probably seen way more international flags than usual
• Let’s recreate some in PGL!
• Each member of your group should choose a different flag. Your task is to recreate it as exactly as possible.
• A list of countries with flags that would be very approachable with our current shapes follows on the next slide
  • You’ll need to search for the flag itself to see what you need to replicate (Wikipedia is great for this)

Country Flag Options

Problem 3: The Drunken Robot

• Determine the middle of your window and save the x and y coordinates. This is your robots current location.
• Draw a 25x25 square at that location (doesn’t need to be centered, but could be!)
  • Make it filled with a fill color of your choice
• Now, for 50 iterations:
  • Determine the next direction (North, South, East or West) randomly
  • Update the robot’s location variables accordingly, assuming they moved exactly 25 pixels in that direction
  • Draw a new square at the robot’s new location (with a different fill color than your starting color)
• Admire your robot’s little drunken walk! Play around with more iterations!

Estimating Pi

• One of the ways that the value of \(\pi\) can be estimated is by looking at the number of random points that strike a circle vs a surrounding box
• Our task here is to both estimate they value of \(\pi\) using random numbers in this fashion, but to also visualize it!

A Solution

from pgl import GWindow, GRect, GOval
import random

WIDTH = 800
HEIGHT = 800

SIZE = 700
DART_SIZE = 10

gw = GWindow(WIDTH, HEIGHT)

background = GRect(
    WIDTH / 2 - SIZE / 2,
    HEIGHT / 2 - SIZE / 2,
    SIZE,
    SIZE
)
background.set_filled(True)
background.set_color('gray')
gw.add(background)

target = GOval(
    WIDTH / 2 - SIZE / 2,
    HEIGHT / 2 - SIZE / 2,
    SIZE,
    SIZE
)
target.set_filled(True)
target.set_color('darkgray')
gw.add(target)

attempts = 1000
successful_strikes = 0
for i in range(attempts):
    x = random.uniform(WIDTH / 2 - SIZE / 2, WIDTH / 2 + SIZE / 2)
    y = random.uniform(HEIGHT / 2 - SIZE / 2, HEIGHT / 2 + SIZE / 2)
    dart = GOval(
        x - DART_SIZE / 2,
        y - DART_SIZE / 2,
        DART_SIZE,
        DART_SIZE
    )
    dart.set_filled(True)
    distance_to_center = (
        (x - WIDTH / 2)**2 + (y - HEIGHT / 2)**2
    ) ** (1/2)
    if distance_to_center < SIZE / 2:
        dart.set_fill_color('red')
        successful_strikes += 1
    else:
        dart.set_fill_color('blue')
    gw.add(dart)

# I forgot this extra factor of 4 in class! That is why it wasn't working initially
print(successful_strikes / attempts * 4 )