Monday 12/05/2011 (12 = One Dozen is a handful for 05 Five Fingers).

Monte Carlo and using the Formula for an Ellipse in honor of WRC Ellipticals.

CS 1025 - Dime Quarter LAC class...

VIP: Throwing 20 Darts - old Monte Carlo Quiz illustrates the concepts of the Monte Carlo simulation approach to estimating an unknown area using uniform random points within a larger known area. If the larger area is not known, you at the very least can estimate the proportion of some enclosed area using Monte Carlo "dart throwing".

powered by NetLogo

view/download model file: DrawOvalMonteCarlo.nlogo

Generate a randomX location and a randomY location for each turtle inside the turtle world, after drawing an Elliptical geometric object. Then choose the hatch either a cow if inside the Oval or build a House if outside the Oval. The turtle that hatched the cow or built the house dies. The count of houses and cows is used to estimate the proportion of the area the OVAL takes up. The entire known area is shown in the COUNT PATCHES Monitor.

Use the SLIDER to run the simulation with different numbers of turtles. 50, 100, 150, ... 950, 1000 are the 20 choices for how many turtles become Monte Carlo darts.

Adjust the height and width of the Ellipse by using the h and w sliders. When h = w, you have a special ellipse, i.e. a circle. Just as a square is a special instance of rectangle, where h = w.

When h is not equal to w, you have an ellipse, also known as an oval, also shaped like an egg. Seems only appropriate or at least poetic for TURTLE agents and LOGO Turtle Graphics.

This section could give some ideas of things for the user to try to do (move sliders, switches, etc.) with the model. Feel free to move the sliders and turn the SWITCH ON and OFF.

Add a slider to draw the ellipse at different speeds, from a delay of 0 to a delay of perhaps 0.1 with the increment being 0.01 and the default being 0.01.

wait 0.01 ;; would become wait drawEllipseDelay ;; drawEllipseDelay slider would allow 0, 0.01, 0.02, 0.03, ... , 0.09, 0.1

This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.

;; Tuesday - February 16 until 12:30 a.m. Wednesday February 17, 2010 globals [locX locY1 locY2 howFar] breed [cows cow] breed [houses house] TO MonteCarlo if count turtles > 0 [ ca prepareIt ] if seePatches [ checkerBoard ] cro howManyTurtles ask-concurrent turtles [ setxy random-xcor random-ycor set color black ifelse abs xcor <= w [ SET locY1 sqrt ( abs (h * h * (1 - (xcor * xcor) / (w * w)) )) SET locY2 0 - locY1 ifelse ycor >= locY2 and ycor <= locY1 [ hatch-cows 1 [ set shape "cow" set color black ] die ] [ hatch-houses 1 [ set shape "house" set color green ] die ] ] [ hatch-houses 1 [ set shape "house" set color green ] die ] ] END TO checkerBoard ask patches [ ifelse remainder (pxcor + pycor) 2 = 0 [ set pcolor white ] [ set pcolor yellow ] ] END TO prepareIt ca cro 2 ask patches [ set pcolor white ] ask-concurrent turtles [ OVAL ] END TO OVAL pu set howFar (2 * w / 300) set locX w setxy locX 0 pd set pen-size 2 set color blue REPEAT 300 [ wait 0.01 set locX xcor - howFar SET locY1 sqrt ( abs (h * h * (1 - (locX * locX) / (w * w)) )) SET locY2 0 - locY1 ifelse (remainder who 2 = 0) [ facexy locX locY1 setxy locX locY1 ] [ facexy locX locY2 setxy locX locY2 ] ;; SET locX locX - howFar ] wait 1 die END