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Shady Sphere: Random point generation on a sphere with function-based labeling

Shady Sphere: Random point generation on a sphere with function-based labeling
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2021-01-11 18:21
FunctionSequenceCoordinate GeometrySolid GeometryProbability & Statistics
This example demonstrates how to generate and plot a set of points related to a spherical geometry (often via a 2D projection/constraint) using randomized sampling and sequence-driven construction. The visualization highlights how the distribution of points emerges from coordinate constraints and function mappings. Key mathematics includes coordinate geometry, functions with parameterized evaluation, random sequences (sampling), distance computation (e.g., via hypot/square-sum-and-root style metrics), and the quadratic-equation idea underlying radius/distance constraints on sphere-like objects. Construction uses Sequence to create index lists, Random to produce sampling parameters, Flatten to simplify nested outputs, Zip to pair indices with values, and Length to control the number of generated items. Geometry is built with Circle to represent the boundary/constraint in the drawing plane, while Textfield is used for labeling function and parameter expressions. Additional commands/objects such as hypot, modf, and arithmetic/mod operations support the numeric transformation from parameters to coordinates and final point placement. Suitable for middle school through early university, especially for lessons on graphing, parametric construction, and understanding how functions and constraints produce structured point distributions.

GeoGebra Commands & Parameters

  1. Sequence((2 * N)) → Lk
  2. Flatten(Zip[Zip[(m, n), n, Lk], m, Lk]) → Lij
  3. Sequence((-N), N - 1) → Lp
  4. Flatten(Zip[Zip[(u, v), v, Lp], u, Lp]) → LC
  5. Random(-6, 6) → Cx
  6. Random(-6, 6) → Cy
  7. Zip(IndexOf[P, LC], P, LC) → LI
  8. Length(Lij) → a
  9. Zip("circleX" + (Text[x(ij)]) + "Y" + (Text[y(ij)]), ij, Lij) → Lname
  10. Circle((-8, -8), R(x((-8, -8)), y((-8, -8)), 1)) → circleX1Y1
  11. Circle((-8, -7), R(x((-8, -7)), y((-8, -7)), 2)) → circleX1Y2
  12. Circle((-8, -6), R(x((-8, -6)), y((-8, -6)), 3)) → circleX1Y3
  13. Circle((-8, -5), R(x((-8, -5)), y((-8, -5)), 4)) → circleX1Y4
  14. Circle((-8, -4), R(x((-8, -4)), y((-8, -4)), 5)) → circleX1Y5
  15. Circle((-8, -3), R(x((-8, -3)), y((-8, -3)), 6)) → circleX1Y6
  16. Circle((-8, -2), R(x((-8, -2)), y((-8, -2)), 7)) → circleX1Y7
  17. Circle((-8, -1), R(x((-8, -1)), y((-8, -1)), 8)) → circleX1Y8
  18. Circle((-8, 0), R(x((-8, 0)), y((-8, 0)), 9)) → circleX1Y9
  19. Circle((-8, 1), R(x((-8, 1)), y((-8, 1)), 10)) → circleX1Y10
  20. Circle((-8, 2), R(x((-8, 2)), y((-8, 2)), 11)) → circleX1Y11
  21. Circle((-8, 3), R(x((-8, 3)), y((-8, 3)), 12)) → circleX1Y12
  22. Circle((-8, 4), R(x((-8, 4)), y((-8, 4)), 13)) → circleX1Y13
  23. Circle((-8, 5), R(x((-8, 5)), y((-8, 5)), 14)) → circleX1Y14
  24. Circle((-8, 6), R(x((-8, 6)), y((-8, 6)), 15)) → circleX1Y15
  25. Circle((-8, 7), R(x((-8, 7)), y((-8, 7)), 16)) → circleX1Y16
  26. Circle((-7, -8), R(x((-7, -8)), y((-7, -8)), 17)) → circleX2Y1
  27. Circle((-7, -7), R(x((-7, -7)), y((-7, -7)), 18)) → circleX2Y2
  28. Circle((-7, -6), R(x((-7, -6)), y((-7, -6)), 19)) → circleX2Y3
  29. Circle((-7, -5), R(x((-7, -5)), y((-7, -5)), 20)) → circleX2Y4
  30. Circle((-7, -4), R(x((-7, -4)), y((-7, -4)), 21)) → circleX2Y5
  31. Circle((-7, -3), R(x((-7, -3)), y((-7, -3)), 22)) → circleX2Y6
  32. Circle((-7, -2), R(x((-7, -2)), y((-7, -2)), 23)) → circleX2Y7
  33. Circle((-7, -1), R(x((-7, -1)), y((-7, -1)), 24)) → circleX2Y8
  34. Circle((-7, 0), R(x((-7, 0)), y((-7, 0)), 25)) → circleX2Y9
  35. Circle((-7, 1), R(x((-7, 1)), y((-7, 1)), 26)) → circleX2Y10
  36. Circle((-7, 2), R(x((-7, 2)), y((-7, 2)), 27)) → circleX2Y11
  37. Circle((-7, 3), R(x((-7, 3)), y((-7, 3)), 28)) → circleX2Y12
  38. Circle((-7, 4), R(x((-7, 4)), y((-7, 4)), 29)) → circleX2Y13
  39. Circle((-7, 5), R(x((-7, 5)), y((-7, 5)), 30)) → circleX2Y14
  40. Circle((-7, 6), R(x((-7, 6)), y((-7, 6)), 31)) → circleX2Y15
  41. Circle((-7, 7), R(x((-7, 7)), y((-7, 7)), 32)) → circleX2Y16
  42. Circle((-6, -8), R(x((-6, -8)), y((-6, -8)), 33)) → circleX3Y1
  43. Circle((-6, -7), R(x((-6, -7)), y((-6, -7)), 34)) → circleX3Y2
  44. Circle((-6, -6), R(x((-6, -6)), y((-6, -6)), 35)) → circleX3Y3
  45. Circle((-6, -5), R(x((-6, -5)), y((-6, -5)), 36)) → circleX3Y4
  46. Circle((-6, -4), R(x((-6, -4)), y((-6, -4)), 37)) → circleX3Y5
  47. Circle((-6, -3), R(x((-6, -3)), y((-6, -3)), 38)) → circleX3Y6
  48. Circle((-6, -2), R(x((-6, -2)), y((-6, -2)), 39)) → circleX3Y7
  49. Circle((-6, -1), R(x((-6, -1)), y((-6, -1)), 40)) → circleX3Y8
  50. Circle((-6, 0), R(x((-6, 0)), y((-6, 0)), 41)) → circleX3Y9
  51. Circle((-6, 1), R(x((-6, 1)), y((-6, 1)), 42)) → circleX3Y10
  52. Circle((-6, 2), R(x((-6, 2)), y((-6, 2)), 43)) → circleX3Y11
  53. Circle((-6, 3), R(x((-6, 3)), y((-6, 3)), 44)) → circleX3Y12
  54. Circle((-6, 4), R(x((-6, 4)), y((-6, 4)), 45)) → circleX3Y13
  55. Circle((-6, 5), R(x((-6, 5)), y((-6, 5)), 46)) → circleX3Y14
  56. Circle((-6, 6), R(x((-6, 6)), y((-6, 6)), 47)) → circleX3Y15
  57. Circle((-6, 7), R(x((-6, 7)), y((-6, 7)), 48)) → circleX3Y16
  58. Circle((-5, -8), R(x((-5, -8)), y((-5, -8)), 49)) → circleX4Y1
  59. Circle((-5, -7), R(x((-5, -7)), y((-5, -7)), 50)) → circleX4Y2
  60. Circle((-5, -6), R(x((-5, -6)), y((-5, -6)), 51)) → circleX4Y3
  61. Circle((-5, -5), R(x((-5, -5)), y((-5, -5)), 52)) → circleX4Y4
  62. Circle((-5, -4), R(x((-5, -4)), y((-5, -4)), 53)) → circleX4Y5
  63. Circle((-5, -3), R(x((-5, -3)), y((-5, -3)), 54)) → circleX4Y6
  64. Circle((-5, -2), R(x((-5, -2)), y((-5, -2)), 55)) → circleX4Y7
  65. Circle((-5, -1), R(x((-5, -1)), y((-5, -1)), 56)) → circleX4Y8
  66. Circle((-5, 0), R(x((-5, 0)), y((-5, 0)), 57)) → circleX4Y9
  67. Circle((-5, 1), R(x((-5, 1)), y((-5, 1)), 58)) → circleX4Y10
  68. Circle((-5, 2), R(x((-5, 2)), y((-5, 2)), 59)) → circleX4Y11
  69. Circle((-5, 3), R(x((-5, 3)), y((-5, 3)), 60)) → circleX4Y12
  70. Circle((-5, 4), R(x((-5, 4)), y((-5, 4)), 61)) → circleX4Y13
  71. Circle((-5, 5), R(x((-5, 5)), y((-5, 5)), 62)) → circleX4Y14
  72. Circle((-5, 6), R(x((-5, 6)), y((-5, 6)), 63)) → circleX4Y15
  73. Circle((-5, 7), R(x((-5, 7)), y((-5, 7)), 64)) → circleX4Y16
  74. Circle((-4, -8), R(x((-4, -8)), y((-4, -8)), 65)) → circleX5Y1
  75. Circle((-4, -7), R(x((-4, -7)), y((-4, -7)), 66)) → circleX5Y2
  76. Circle((-4, -6), R(x((-4, -6)), y((-4, -6)), 67)) → circleX5Y3
  77. Circle((-4, -5), R(x((-4, -5)), y((-4, -5)), 68)) → circleX5Y4
  78. Circle((-4, -4), R(x((-4, -4)), y((-4, -4)), 69)) → circleX5Y5
  79. Circle((-4, -3), R(x((-4, -3)), y((-4, -3)), 70)) → circleX5Y6
  80. Circle((-4, -2), R(x((-4, -2)), y((-4, -2)), 71)) → circleX5Y7
  81. Circle((-4, -1), R(x((-4, -1)), y((-4, -1)), 72)) → circleX5Y8
  82. Circle((-4, 0), R(x((-4, 0)), y((-4, 0)), 73)) → circleX5Y9
  83. Circle((-4, 1), R(x((-4, 1)), y((-4, 1)), 74)) → circleX5Y10
  84. Circle((-4, 2), R(x((-4, 2)), y((-4, 2)), 75)) → circleX5Y11
  85. Circle((-4, 3), R(x((-4, 3)), y((-4, 3)), 76)) → circleX5Y12
  86. Circle((-4, 4), R(x((-4, 4)), y((-4, 4)), 77)) → circleX5Y13
  87. Circle((-4, 5), R(x((-4, 5)), y((-4, 5)), 78)) → circleX5Y14
  88. Circle((-4, 6), R(x((-4, 6)), y((-4, 6)), 79)) → circleX5Y15
  89. Circle((-4, 7), R(x((-4, 7)), y((-4, 7)), 80)) → circleX5Y16
  90. Circle((-3, -8), R(x((-3, -8)), y((-3, -8)), 81)) → circleX6Y1
  91. Circle((-3, -7), R(x((-3, -7)), y((-3, -7)), 82)) → circleX6Y2
  92. Circle((-3, -6), R(x((-3, -6)), y((-3, -6)), 83)) → circleX6Y3
  93. Circle((-3, -5), R(x((-3, -5)), y((-3, -5)), 84)) → circleX6Y4
  94. Circle((-3, -4), R(x((-3, -4)), y((-3, -4)), 85)) → circleX6Y5
  95. Circle((-3, -3), R(x((-3, -3)), y((-3, -3)), 86)) → circleX6Y6
  96. Circle((-3, -2), R(x((-3, -2)), y((-3, -2)), 87)) → circleX6Y7
  97. Circle((-3, -1), R(x((-3, -1)), y((-3, -1)), 88)) → circleX6Y8
  98. Circle((-3, 0), R(x((-3, 0)), y((-3, 0)), 89)) → circleX6Y9
  99. Circle((-3, 1), R(x((-3, 1)), y((-3, 1)), 90)) → circleX6Y10
  100. Circle((-3, 2), R(x((-3, 2)), y((-3, 2)), 91)) → circleX6Y11
  101. Circle((-3, 3), R(x((-3, 3)), y((-3, 3)), 92)) → circleX6Y12
  102. Circle((-3, 4), R(x((-3, 4)), y((-3, 4)), 93)) → circleX6Y13
  103. Circle((-3, 5), R(x((-3, 5)), y((-3, 5)), 94)) → circleX6Y14
  104. Circle((-3, 6), R(x((-3, 6)), y((-3, 6)), 95)) → circleX6Y15
  105. Circle((-3, 7), R(x((-3, 7)), y((-3, 7)), 96)) → circleX6Y16
  106. Circle((-2, -8), R(x((-2, -8)), y((-2, -8)), 97)) → circleX7Y1
  107. Circle((-2, -7), R(x((-2, -7)), y((-2, -7)), 98)) → circleX7Y2
  108. Circle((-2, -6), R(x((-2, -6)), y((-2, -6)), 99)) → circleX7Y3
  109. Circle((-2, -5), R(x((-2, -5)), y((-2, -5)), 100)) → circleX7Y4
  110. Circle((-2, -4), R(x((-2, -4)), y((-2, -4)), 101)) → circleX7Y5
  111. Circle((-2, -3), R(x((-2, -3)), y((-2, -3)), 102)) → circleX7Y6
  112. Circle((-2, -2), R(x((-2, -2)), y((-2, -2)), 103)) → circleX7Y7
  113. Circle((-2, -1), R(x((-2, -1)), y((-2, -1)), 104)) → circleX7Y8
  114. Circle((-2, 0), R(x((-2, 0)), y((-2, 0)), 105)) → circleX7Y9
  115. Circle((-2, 1), R(x((-2, 1)), y((-2, 1)), 106)) → circleX7Y10
  116. Circle((-2, 2), R(x((-2, 2)), y((-2, 2)), 107)) → circleX7Y11
  117. Circle((-2, 3), R(x((-2, 3)), y((-2, 3)), 108)) → circleX7Y12
  118. Circle((-2, 4), R(x((-2, 4)), y((-2, 4)), 109)) → circleX7Y13
  119. Circle((-2, 5), R(x((-2, 5)), y((-2, 5)), 110)) → circleX7Y14
  120. Circle((-2, 6), R(x((-2, 6)), y((-2, 6)), 111)) → circleX7Y15
  121. Circle((-2, 7), R(x((-2, 7)), y((-2, 7)), 112)) → circleX7Y16
  122. Circle((-1, -8), R(x((-1, -8)), y((-1, -8)), 113)) → circleX8Y1
  123. Circle((-1, -7), R(x((-1, -7)), y((-1, -7)), 114)) → circleX8Y2
  124. Circle((-1, -6), R(x((-1, -6)), y((-1, -6)), 115)) → circleX8Y3
  125. Circle((-1, -5), R(x((-1, -5)), y((-1, -5)), 116)) → circleX8Y4
  126. Circle((-1, -4), R(x((-1, -4)), y((-1, -4)), 117)) → circleX8Y5
  127. Circle((-1, -3), R(x((-1, -3)), y((-1, -3)), 118)) → circleX8Y6
  128. Circle((-1, -2), R(x((-1, -2)), y((-1, -2)), 119)) → circleX8Y7
  129. Circle((-1, -1), R(x((-1, -1)), y((-1, -1)), 120)) → circleX8Y8
  130. Circle((-1, 0), R(x((-1, 0)), y((-1, 0)), 121)) → circleX8Y9
  131. Circle((-1, 1), R(x((-1, 1)), y((-1, 1)), 122)) → circleX8Y10
  132. Circle((-1, 2), R(x((-1, 2)), y((-1, 2)), 123)) → circleX8Y11
  133. Circle((-1, 3), R(x((-1, 3)), y((-1, 3)), 124)) → circleX8Y12
  134. Circle((-1, 4), R(x((-1, 4)), y((-1, 4)), 125)) → circleX8Y13
  135. Circle((-1, 5), R(x((-1, 5)), y((-1, 5)), 126)) → circleX8Y14
  136. Circle((-1, 6), R(x((-1, 6)), y((-1, 6)), 127)) → circleX8Y15
  137. Circle((-1, 7), R(x((-1, 7)), y((-1, 7)), 128)) → circleX8Y16
  138. Circle((0, -8), R(x((0, -8)), y((0, -8)), 129)) → circleX9Y1
  139. Circle((0, -7), R(x((0, -7)), y((0, -7)), 130)) → circleX9Y2
  140. Circle((0, -6), R(x((0, -6)), y((0, -6)), 131)) → circleX9Y3
  141. Circle((0, -5), R(x((0, -5)), y((0, -5)), 132)) → circleX9Y4
  142. Circle((0, -4), R(x((0, -4)), y((0, -4)), 133)) → circleX9Y5
  143. Circle((0, -3), R(x((0, -3)), y((0, -3)), 134)) → circleX9Y6
  144. Circle((0, -2), R(x((0, -2)), y((0, -2)), 135)) → circleX9Y7
  145. Circle((0, -1), R(x((0, -1)), y((0, -1)), 136)) → circleX9Y8
  146. Circle((0, 0), R(x((0, 0)), y((0, 0)), 137)) → circleX9Y9
  147. Circle((0, 1), R(x((0, 1)), y((0, 1)), 138)) → circleX9Y10
  148. Circle((0, 2), R(x((0, 2)), y((0, 2)), 139)) → circleX9Y11
  149. Circle((0, 3), R(x((0, 3)), y((0, 3)), 140)) → circleX9Y12
  150. Circle((0, 4), R(x((0, 4)), y((0, 4)), 141)) → circleX9Y13
  151. Circle((0, 5), R(x((0, 5)), y((0, 5)), 142)) → circleX9Y14
  152. Circle((0, 6), R(x((0, 6)), y((0, 6)), 143)) → circleX9Y15
  153. Circle((0, 7), R(x((0, 7)), y((0, 7)), 144)) → circleX9Y16
  154. Circle((1, -8), R(x((1, -8)), y((1, -8)), 145)) → circleX10Y1
  155. Circle((1, -7), R(x((1, -7)), y((1, -7)), 146)) → circleX10Y2
  156. Circle((1, -6), R(x((1, -6)), y((1, -6)), 147)) → circleX10Y3
  157. Circle((1, -5), R(x((1, -5)), y((1, -5)), 148)) → circleX10Y4
  158. Circle((1, -4), R(x((1, -4)), y((1, -4)), 149)) → circleX10Y5
  159. Circle((1, -3), R(x((1, -3)), y((1, -3)), 150)) → circleX10Y6
  160. Circle((1, -2), R(x((1, -2)), y((1, -2)), 151)) → circleX10Y7
  161. Circle((1, -1), R(x((1, -1)), y((1, -1)), 152)) → circleX10Y8
  162. Circle((1, 0), R(x((1, 0)), y((1, 0)), 153)) → circleX10Y9
  163. Circle((1, 1), R(x((1, 1)), y((1, 1)), 154)) → circleX10Y10
  164. Circle((1, 2), R(x((1, 2)), y((1, 2)), 155)) → circleX10Y11
  165. Circle((1, 3), R(x((1, 3)), y((1, 3)), 156)) → circleX10Y12
  166. Circle((1, 4), R(x((1, 4)), y((1, 4)), 157)) → circleX10Y13
  167. Circle((1, 5), R(x((1, 5)), y((1, 5)), 158)) → circleX10Y14
  168. Circle((1, 6), R(x((1, 6)), y((1, 6)), 159)) → circleX10Y15
  169. Circle((1, 7), R(x((1, 7)), y((1, 7)), 160)) → circleX10Y16
  170. Circle((2, -8), R(x((2, -8)), y((2, -8)), 161)) → circleX11Y1
  171. Circle((2, -7), R(x((2, -7)), y((2, -7)), 162)) → circleX11Y2
  172. Circle((2, -6), R(x((2, -6)), y((2, -6)), 163)) → circleX11Y3
  173. Circle((2, -5), R(x((2, -5)), y((2, -5)), 164)) → circleX11Y4
  174. Circle((2, -4), R(x((2, -4)), y((2, -4)), 165)) → circleX11Y5
  175. Circle((2, -3), R(x((2, -3)), y((2, -3)), 166)) → circleX11Y6
  176. Circle((2, -2), R(x((2, -2)), y((2, -2)), 167)) → circleX11Y7
  177. Circle((2, -1), R(x((2, -1)), y((2, -1)), 168)) → circleX11Y8
  178. Circle((2, 0), R(x((2, 0)), y((2, 0)), 169)) → circleX11Y9
  179. Circle((2, 1), R(x((2, 1)), y((2, 1)), 170)) → circleX11Y10
  180. Circle((2, 2), R(x((2, 2)), y((2, 2)), 171)) → circleX11Y11
  181. Circle((2, 3), R(x((2, 3)), y((2, 3)), 172)) → circleX11Y12
  182. Circle((2, 4), R(x((2, 4)), y((2, 4)), 173)) → circleX11Y13
  183. Circle((2, 5), R(x((2, 5)), y((2, 5)), 174)) → circleX11Y14
  184. Circle((2, 6), R(x((2, 6)), y((2, 6)), 175)) → circleX11Y15
  185. Circle((2, 7), R(x((2, 7)), y((2, 7)), 176)) → circleX11Y16
  186. Circle((3, -8), R(x((3, -8)), y((3, -8)), 177)) → circleX12Y1
  187. Circle((3, -7), R(x((3, -7)), y((3, -7)), 178)) → circleX12Y2
  188. Circle((3, -6), R(x((3, -6)), y((3, -6)), 179)) → circleX12Y3
  189. Circle((3, -5), R(x((3, -5)), y((3, -5)), 180)) → circleX12Y4
  190. Circle((3, -4), R(x((3, -4)), y((3, -4)), 181)) → circleX12Y5
  191. Circle((3, -3), R(x((3, -3)), y((3, -3)), 182)) → circleX12Y6
  192. Circle((3, -2), R(x((3, -2)), y((3, -2)), 183)) → circleX12Y7
  193. Circle((3, -1), R(x((3, -1)), y((3, -1)), 184)) → circleX12Y8
  194. Circle((3, 0), R(x((3, 0)), y((3, 0)), 185)) → circleX12Y9
  195. Circle((3, 1), R(x((3, 1)), y((3, 1)), 186)) → circleX12Y10
  196. Circle((3, 2), R(x((3, 2)), y((3, 2)), 187)) → circleX12Y11
  197. Circle((3, 3), R(x((3, 3)), y((3, 3)), 188)) → circleX12Y12
  198. Circle((3, 4), R(x((3, 4)), y((3, 4)), 189)) → circleX12Y13
  199. Circle((3, 5), R(x((3, 5)), y((3, 5)), 190)) → circleX12Y14
  200. Circle((3, 6), R(x((3, 6)), y((3, 6)), 191)) → circleX12Y15
  201. Circle((3, 7), R(x((3, 7)), y((3, 7)), 192)) → circleX12Y16
  202. Circle((4, -8), R(x((4, -8)), y((4, -8)), 193)) → circleX13Y1
  203. Circle((4, -7), R(x((4, -7)), y((4, -7)), 194)) → circleX13Y2
  204. Circle((4, -6), R(x((4, -6)), y((4, -6)), 195)) → circleX13Y3
  205. Circle((4, -5), R(x((4, -5)), y((4, -5)), 196)) → circleX13Y4
  206. Circle((4, -4), R(x((4, -4)), y((4, -4)), 197)) → circleX13Y5
  207. Circle((4, -3), R(x((4, -3)), y((4, -3)), 198)) → circleX13Y6
  208. Circle((4, -2), R(x((4, -2)), y((4, -2)), 199)) → circleX13Y7
  209. Circle((4, -1), R(x((4, -1)), y((4, -1)), 200)) → circleX13Y8
  210. Circle((4, 0), R(x((4, 0)), y((4, 0)), 201)) → circleX13Y9
  211. Circle((4, 1), R(x((4, 1)), y((4, 1)), 202)) → circleX13Y10
  212. Circle((4, 2), R(x((4, 2)), y((4, 2)), 203)) → circleX13Y11
  213. Circle((4, 3), R(x((4, 3)), y((4, 3)), 204)) → circleX13Y12
  214. Circle((4, 4), R(x((4, 4)), y((4, 4)), 205)) → circleX13Y13
  215. Circle((4, 5), R(x((4, 5)), y((4, 5)), 206)) → circleX13Y14
  216. Circle((4, 6), R(x((4, 6)), y((4, 6)), 207)) → circleX13Y15
  217. Circle((4, 7), R(x((4, 7)), y((4, 7)), 208)) → circleX13Y16
  218. Circle((5, -8), R(x((5, -8)), y((5, -8)), 209)) → circleX14Y1
  219. Circle((5, -7), R(x((5, -7)), y((5, -7)), 210)) → circleX14Y2
  220. Circle((5, -6), R(x((5, -6)), y((5, -6)), 211)) → circleX14Y3
  221. Circle((5, -5), R(x((5, -5)), y((5, -5)), 212)) → circleX14Y4
  222. Circle((5, -4), R(x((5, -4)), y((5, -4)), 213)) → circleX14Y5
  223. Circle((5, -3), R(x((5, -3)), y((5, -3)), 214)) → circleX14Y6
  224. Circle((5, -2), R(x((5, -2)), y((5, -2)), 215)) → circleX14Y7
  225. Circle((5, -1), R(x((5, -1)), y((5, -1)), 216)) → circleX14Y8
  226. Circle((5, 0), R(x((5, 0)), y((5, 0)), 217)) → circleX14Y9
  227. Circle((5, 1), R(x((5, 1)), y((5, 1)), 218)) → circleX14Y10
  228. Circle((5, 2), R(x((5, 2)), y((5, 2)), 219)) → circleX14Y11
  229. Circle((5, 3), R(x((5, 3)), y((5, 3)), 220)) → circleX14Y12
  230. Circle((5, 4), R(x((5, 4)), y((5, 4)), 221)) → circleX14Y13
  231. Circle((5, 5), R(x((5, 5)), y((5, 5)), 222)) → circleX14Y14
  232. Circle((5, 6), R(x((5, 6)), y((5, 6)), 223)) → circleX14Y15
  233. Circle((5, 7), R(x((5, 7)), y((5, 7)), 224)) → circleX14Y16
  234. Circle((6, -8), R(x((6, -8)), y((6, -8)), 225)) → circleX15Y1
  235. Circle((6, -7), R(x((6, -7)), y((6, -7)), 226)) → circleX15Y2
  236. Circle((6, -6), R(x((6, -6)), y((6, -6)), 227)) → circleX15Y3
  237. Circle((6, -5), R(x((6, -5)), y((6, -5)), 228)) → circleX15Y4
  238. Circle((6, -4), R(x((6, -4)), y((6, -4)), 229)) → circleX15Y5
  239. Circle((6, -3), R(x((6, -3)), y((6, -3)), 230)) → circleX15Y6
  240. Circle((6, -2), R(x((6, -2)), y((6, -2)), 231)) → circleX15Y7
  241. Circle((6, -1), R(x((6, -1)), y((6, -1)), 232)) → circleX15Y8
  242. Circle((6, 0), R(x((6, 0)), y((6, 0)), 233)) → circleX15Y9
  243. Circle((6, 1), R(x((6, 1)), y((6, 1)), 234)) → circleX15Y10
  244. Circle((6, 2), R(x((6, 2)), y((6, 2)), 235)) → circleX15Y11
  245. Circle((6, 3), R(x((6, 3)), y((6, 3)), 236)) → circleX15Y12
  246. Circle((6, 4), R(x((6, 4)), y((6, 4)), 237)) → circleX15Y13
  247. Circle((6, 5), R(x((6, 5)), y((6, 5)), 238)) → circleX15Y14
  248. Circle((6, 6), R(x((6, 6)), y((6, 6)), 239)) → circleX15Y15
  249. Circle((6, 7), R(x((6, 7)), y((6, 7)), 240)) → circleX15Y16
  250. Circle((7, -8), R(x((7, -8)), y((7, -8)), 241)) → circleX16Y1
  251. Circle((7, -7), R(x((7, -7)), y((7, -7)), 242)) → circleX16Y2
  252. Circle((7, -6), R(x((7, -6)), y((7, -6)), 243)) → circleX16Y3
  253. Circle((7, -5), R(x((7, -5)), y((7, -5)), 244)) → circleX16Y4
  254. Circle((7, -4), R(x((7, -4)), y((7, -4)), 245)) → circleX16Y5
  255. Circle((7, -3), R(x((7, -3)), y((7, -3)), 246)) → circleX16Y6
  256. Circle((7, -2), R(x((7, -2)), y((7, -2)), 247)) → circleX16Y7
  257. Circle((7, -1), R(x((7, -1)), y((7, -1)), 248)) → circleX16Y8
  258. Circle((7, 0), R(x((7, 0)), y((7, 0)), 249)) → circleX16Y9
  259. Circle((7, 1), R(x((7, 1)), y((7, 1)), 250)) → circleX16Y10
  260. Circle((7, 2), R(x((7, 2)), y((7, 2)), 251)) → circleX16Y11
  261. Circle((7, 3), R(x((7, 3)), y((7, 3)), 252)) → circleX16Y12
  262. Circle((7, 4), R(x((7, 4)), y((7, 4)), 253)) → circleX16Y13
  263. Circle((7, 5), R(x((7, 5)), y((7, 5)), 254)) → circleX16Y14
  264. Circle((7, 6), R(x((7, 6)), y((7, 6)), 255)) → circleX16Y15
  265. Circle((7, 7), R(x((7, 7)), y((7, 7)), 256)) → circleX16Y16
  266. Textfield(f) → InputBox1

AI Drawing Prompt Reference

Create a grid of points with integer coordinates ranging from -8 to 7 in both x and y directions. At each grid point, draw a circle whose radius is determined by a function of the point's coordinates and a sequential index. Additionally, generate a set of random points within the same coordinate range, and label each random point with a name that references its corresponding grid point. The overall composition shows a structured arrangement of circles overlaid with randomly placed labeled points, illustrating a relationship between deterministic grid-based geometry and stochastic sampling.
The prompt above was compiled from the original drawing commands and is for reference only.