CS 1025 Computational Modeling and Simulation

Monte Carlo simulations - estimating area by throwing darts


  1. Monte Carlo - review of Wednesday, November 14th class. How to think about the known and the unknown and do algebra with the general formula. Dinosaur/Shark/Star Wars Fruit Snacks tossing solution to Area of the Contruction paper.
     
      1. (x, y) what are the coordinates of a randomly generated point?
    
      2. Where is the randomly generated point located?  
              Inside or outside the region of interest?
    
      3. How many points were generated?
    
      4. What proportion of the points where within each area of interest?
    
      5. What is the known area?
    
      6. What is the equation?
    
      7. What are the known parts of the equation for this particular problem?  
         What is the unknown we are trying to find?
         Is some algebra needed or can the equation be used as is?
    
  2. Monte Carlo with NetLogo - 33 by 33 grid, Cows and Houses, not to be confused with cows in houses instead of barns!

  3. Monte Carlo concepts and problems. MonteCarlo20darts.pdf: Throwing 20 darts, throwing 100 darts, estimating area of an ellipse, estimating area A, B, C and D when a line is involved. y = mx + b. The line has slope m and intercept b.

    Netlogo TURTLES randomly scatter, then turn into either a COW or a HOUSE depending on whether they hit the BULLS EYE or missed the oval shaped bulls eye.





Monte Carlo concepts will be on TEST TWO
Throwing Darts to determine an AREA.

MONTE CARLO QUESTIONS: Throwing Monte Carlo Darts or randomly scattering out turtles! :-)


  • Monte Carlo - given a diagram and graphical setup of an area, be able to determine what the area of below the function or between two functions is by using the Monte Carlo method.

    Know and understand the formula for coming up with a Monte Carlo estimated area when you know the proportion of or the actual count of "darts" that landed inside the area of interest.

  • Example:  Look at the following diagram which shows a solid point for every dart that was thrown
              and where it hit inside the target area.  The target area is the rectangle there you see
              that goes from x = 1 to x = 3 and from y = 4 to y = 8.
               
              (Note: for practical purposes, only 16 or 20 darts were thrown 
                                                   in the examples shown here).
       
              Calculate what the estimated area of the region above function g 
                                                          and below function h would be?  (The area BETWEEN function g and function h).  
              Please show your work and calculations.
              I need to see your process of arriving at the result.
              You will get partial credit if your equation is correct, but you just had a simple calculation, arithmetic error.
              You will NOT get full credit for just having the correct answer, so show the process for that reason too.