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--- dev:quiz_ulam [2015/06/28 17:43] – xychen
+++ dev:quiz_ulam [2015/06/28 17:52] (current) – xychen
@@ Line 79: / Line 79: @@
 {{:dev:4base_500.png?280|}} {{:dev:4shot_600.png?280|}} {{:dev:4grid_500.png?280|}}
 nearly 1/4 data in the ''{2C2}'' experiments are invalid because of they hit the boundary. To rule out the influence of th missing data points(those hit the boundary), we ran the experiments on bigger simulator again. The left graph is 516 //Base Case// runs on ''{4C4}'' simulator after 10 kAEPS. Average distance for //Base Case// is 21.1. Standard deviation is 11.8. The middle graph is 604 //Shot Case// runs on ''{4C4}'' simulator. Average distance for //Shot Case// is 21.8. Standard deviation is 11.9.  The right graph is 521 //Grid Case// runs on ''{4C4}''. Average distance for //Grid Case// is 23.1. Standard deviation is 13.0.
-In the bigger simulator and less time length, we had no data hitting the boundary. The ''{4C4}'' average distance we got seems greater than the ''{2C2}'' average distance. However, nearly 1/3 of the ''{2C2}'' data fell out of the edge. So the actual average distance in ''{2C2}'' should be greater than the data shows. In both experiments, we can see the grid helped to extend the range a ''Pair'' traversed. The extension in ''{2C2}'' seems to be less than 5% (from 18.8 to 19.4) because more data points fell out of the edge. In ''{4C4}'' experiments, the average distances are extended nearly by 9% (from 21.1 to 23.1). This shows that the some //pulses// that travel faster than //walks// are produced in the grid.
+In the bigger simulator and less time length, we had no data hitting the boundary. The ''{4C4}'' average distance we got seems greater than the ''{2C2}'' average distance. However, nearly 1/4 of the ''{2C2}'' data fell out of the edge. So the actual average distance in ''{2C2}'' should be greater than the data shows. In both experiments, we can see the grid helped to extend the range a ''Pair'' traversed. The extension in ''{2C2}'' seems to be less than 5% (from 18.8 to 19.4) because more data points fell out of the edge. In ''{4C4}'' experiments, the average distances are extended nearly by 9% (from 21.1 to 23.1). This shows that the some //pulses// that travel faster than //walks// are produced in the grid.
 The end-positions of the experiments didn't show obvious bias. That's fair because of the initial layout of our experiments. When ''Boxes'' are evenly placed in grid pattern, they //attract// the ''Pairs'' evenly, which will produce no bias. When ''Boxes'' are placed in a line, they are too sparse to //trap// ''Pairs''. This did not produce bias either. In the following experiment, we will place a bunch of ''Boxes'' in the 1st quadrant. This cluster of ''Boxes'' will //attract// the first ''Pair'' and produce more ''Pairs''. Then, the end-positions will show obvious favor to the 1st quadrant.
+{{:dev:4overlay_500.png?350|}}
+The above graph is what we saw if we put the three pictures together. If the end-positions of ''Pairs'' are not surprising, how about the ''Boxes''? Did they still remain in line or in grid? How they were messed up by the ''Pair''?