Summary

Table[ListPlot[Part[smoothedDarts, 1 ;; max], AspectRatio -> 1, 
  PlotStyle -> {PointSize[Small], Blue}, 
  PlotRange -> {{0, 1}, {0, 1}}, 
  PlotLabel -> 
   TraditionalForm[max "Randomly Selected Stratified Points"], 
  Frame -> True, ImageSize -> {400, 400}], {max, 100, Length[darts], 
  Length[darts]/100}], 

Camera location	38° 54′ 14.56″ N, 77° 02′ 53.31″ W	View this and other nearby images on: OpenStreetMap	38.904045; -77.048141

(*This mathematical image was created with Mathematica. The stratification process redistributes the random elements into a \ relatively homogeneous group and then samples randomly. Every element \ in the original set is uniquely reassigned to one stratum. Source code for this image is available below.*) \ tinyColor[color_, point_] := {PointSize[Small], color, Point[point]} colorChoose[point_] := tinyColor[Blue, point]

Clear[r, n]; r = 100; n = r^2; darts = RandomReal[{0, 1}, {n, 2}]; coloredDarts = ParallelMap[colorChoose, darts];

Clear[smoothedDarts, tempPoints] subGrouper = Table[i, {i, 0, r - 1}]; shiftyGuy = Flatten[Tuples[subGrouper, 2]]; tempPoints = Partition[(shiftyGuy + Flatten[darts])*(1/r), 2];

smoothedDarts = RandomSample[tempPoints, n];

Export["~/Desktop/stratifiedPoints.gif",

Table[ListPlot[Part[smoothedDarts, 1 ;; max], AspectRatio -> 1, 
  PlotStyle -> {PointSize[Small], Blue}, 
  PlotRange -> {{0, 1}, {0, 1}}, 
  PlotLabel -> 
   TraditionalForm[max "Randomly Selected Stratified Points"], 
  Frame -> True, ImageSize -> {400, 400}], {max, 100, Length[darts], 
  Length[darts]/100}], 
"DisplayDurations" -> ConstantArray[1, 9]~Join~{3}]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original. https://creativecommons.org/licenses/by-sa/3.0 CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

 This diagram was created with Mathematica