![]() Instead of leaping out of the box, the number at the top-left corner of the plot - the value of the y-axis - updates and the histogram is redrawn for a larger scale. What happens when it reaches the top? More and more combinations are coming but there is no room to count them. How many 9-blocks do you need to sample before the histogram begins to look like the Combinations Tower? NETLOGO FEATURES THINGS TO TRYĬompare between the histogram you are getting and the Combinations Tower. Finally, there is a higher chance of getting 9-blocks that have 1 or 8 green squares as compared to 9-blocks that have 0 or 9 green squares. Also, there is a higher chance of getting 9-blocks that have 2 or 7 green squares as compared to 9-blocks that have 1 or 8 green squares. Likewise, there is a higher chance of getting 9-blocks that have 3 or 6 green squares as compared to 9-blocks that have 2 or 7 green squares. This shows us that there is a higher chance of getting 9-blocks that have 4 or 5 green squares as compared to 9-blocks that have 3 or 6 green squares. ![]() Pretty soon, the central columns grow taller than other columns. THINGS TO NOTICEĪs you run this model, the histogram grows. 'how many trials' - shows how many times the model has chosen random 9-blocks in this experiment (so it's also showing how many items we have in the list that is being plotted every run). ![]() '# target color' - shows how many patches are green. Notice how the monitor '# target color' updates per each target color that is added. This is meant to remind us that even though we are looking at 9-blocks, actually each square chooses its color independently of other squares. Also, there will be a pause between 9-blocks, as though the lights were switched off for a moment. 'one-by-one-choices?' - when On, each square will settle on its color at a different moment. It is set to work "forever," that is, it will repeat until you press it again. So you will get a single 9-block and a short column in the histogram. 'Go' - activates the procedures just once. 'Setup - initializes the variables and erases the plot. Over many runs, the histogram begins to look bell-shaped, just like the Combinations Tower that you may have built in your classroom and just like the tower in the 9-Block Stalagmite model. , 8 green squares, and 9 green squares (for a total of 10 possible columns). The columns or bars in this histogram represent how many 9-blocks have occurred with 0 green squares, 1 green square, 2 green squares. The entire list is plotted as a histogram at each run. This number is added to a list that grows in length from run to run. At every run through Go, the number of green patches in the block is counted up. This "coin" works as follows: The patch chooses randomly between "0" and "1." If it got "1," it becomes green on this run, but if it got "0," it becomes blue on this run. HOW IT WORKSĪt every iteration through Go, each patch "flips a coin" to decide whether it should be green or blue. For more information about the ProbLab Curriculum please refer to. The ProbLab Curriculum is currently under development at the CCL. This model is a part of the ProbLab curriculum. Finally, the plot shows the number of green squares and not the percentage of green squares out of all the squares. Also, the probability of a patch being either green or blue is always. Here, your green/blue combinations are always of size 3 by 3. The 9-Blocks model is a simplified version of the Stochastic Patchwork model. jpg's dimensions as necessary to maximize the resemblance between the histogram and the. (This JPEG will be available with ProbLab curricular material.) Place this JPEG alongside the 9-Blocks histogram, to its right, editing the. To better see the resemblance between the Combinations Tower and 9-Blocks histogram, you can either open another NetLogo window in the 9-Block Stalagmite model or open a JPEG of the 9-Block Stalagmite model as it looks when the entire sample space has been found. How can that be? That is the theme question of this model. In the plot window, a tall histogram grows that has the same shape as the Combinations Tower. Whereas building the Combinations Tower is a form of theoretical probability - combinatorial analysis - the 9-Block model complements with empirical probability of the same 3-by-3 object. You can also Try running it in NetLogo Webĩ-Blocks accompanies classroom work on the Combinations Tower, the giant bell-shaped histogram of all the 512 different green/blue combinations of the 3-by-3 array. If you download the NetLogo application, this model is included. It has not yet been tested and polished as thoroughly as our other models. Sample Models/Mathematics/Probability/ProbLab/Unverified Beginners Interactive NetLogo Dictionary (BIND)
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