COS 126

1
COS 126 Atomic Theory of Matter
2
Atomic Theory Overview

• Brownian Motion
• Random collision of molecules
• Displacement over time fits a Gaussian
  distribution

3
Atomic Theory Overview

• Avogadros Number
• Number of atoms needed to equal substances atomic
  mass in grams
• NA atoms of Carbon-12 12 grams
• Can calculate from Brownian Motion
• Variance of Gaussian distribution is a function
  of resistance in water, number of molecules

4
Bead.java

• Represent particles (beads) in water
• API
• public Bead()
• public void add(int i, int j)
• public int mass() // number of pixels
• public double distanceTo(Bead b) // from center
  (average)
• public String toString()
• Only need 3 values to efficiently store
• Thoroughly test (simple main)

5
BeadFinder.java

• Locate all beads in a given image
• API
• public BeadFinder(Picture picture, double
  threshold)
• Calculate luminance (see Luminance.java, 3.1)
• Count pixels with at luminance gt threshold
• Find beads with DFS (see Percolation.java, 2.4)
• The hard part, next slide
• public Bead getBeads(int minSize)
• Returns all beads with at least minSize pixels
• Array must be of size equal to number of beads

6
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

7
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

8
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

9
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

10
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

11
Bead Finder - Depth First Search

• Use boolean array to mark visited
• Traverse image
• Dark pixel mark as visited, continue
• Light pixel create new bead, call dfs
• DFS algorithm
• If pixel out-of-bounds, return
• If pixel has been visited, return
• If pixel is dark, mark return
• Add pixel to current bead, mark as visited
• Recursively visit up, down, left, right

12
BeadTracker.java

• Track beads between successive images
• Single main function
• Take in a series of images
• Output distance traversed by all beads for each
  time-step
• For each bead found at time t1, find closest
  bead at time t and calculate distance
• Not the other way around!
• Dont include if distance gt 25 pixels (new bead)

13
Avogadro.java

• Analyze Brownian motion of all calculated
  displacements
• Lots of crazy formulas, all given, pretty
  straightforward
• Be careful about units in the math, convert
  pixels to meters, etc.

14
Random Thoughts

• BeadTracker and Avogadro are separate clients,
  must recompile both
• Can still do Avogadro without other parts
  working, use sample input
• Only keep at most two pictures open at a time
  (run out of memory otherwise)
• Output format - System.out.printf()
• "6.3f" -gt _2.354
• "10.4e" -gt 1.2535e-23