Level 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 4 4 4 4 5 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 4 4 4 4 5

Equilateral Triangles Sawtooth Region (height determined by requirement that triangles are equilateral, overlaps set to (2^(-m))/10)






















height 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.1000 0.0100 0.0010 0.0005 0.0010 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.0005 0.1000 0.0100 0.0010 0.1000 0.0100 0.0010 0.0005 0.0010

Level: 2 2 2 2 3 3 3 3 4 4 4 4 Level: 2 2 2 2 3 3 3 3 4 4 4 4
refinements 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 n^2 n Refinements:1 2 3 4 1 2 3 4 1 2 3 4 Refinements:1 2 3 4 1 2 3 4 1 2 3 4


0.000
0.000


0.000 0.000

0.000

0.000



0.000



















0 0 0.000 0.000
0.000




0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

6.256 7.155 7.550 8.017 5.093 6.996 7.229 7.326 3.836 6.782 7.060 7.155 2.867 6.341 6.981 3.795 6.768 7.011 7.061 6.931 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 1 4.905 4.823 4.790 4.777 4.868 4.789 4.756 4.743 4.828 4.749 4.717 4.703 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

23.467 26.916 29.096 31.996 20.023 27.616 28.606 29.123 15.210 27.041 28.154 28.543 11.388 25.345 27.902 15.046 26.987 27.957 28.160 27.704 3.751 3.762 3.854 3.991 3.931 3.947 3.957 3.975 3.965 3.987 3.988 3.989 3.973 3.997 3.997 3.965 3.987 3.987 3.988 3.997 4 2 17.980 17.662 17.535 17.483 19.097 18.782 18.655 18.602 19.218 18.903 18.776 18.724 3.665 3.662 3.661 3.660 3.923 3.922 3.922 3.922 3.981 3.981 3.981 3.981

45.256 52.154 56.017 60.827 43.675 60.656 63.040 64.508 33.701 60.510 63.022 63.921 25.325 56.948 62.698 33.341 60.387 62.567 63.035 62.251 7.234 7.289 7.419 7.587 8.575 8.670 8.721 8.805 8.786 8.922 8.927 8.933 8.834 8.980 8.981 8.786 8.922 8.924 8.927 8.981 9 3 33.418 32.790 32.539 32.436 41.513 40.808 40.525 40.408 42.900 42.191 41.906 41.787 6.813 6.798 6.793 6.790 8.527 8.522 8.520 8.519 8.886 8.885 8.884 8.884

294.835 327.674 331.873 333.511 73.960 103.746 108.178 111.071 58.625 106.725 111.207 112.857 44.286 101.047 111.258 58.004 106.506 110.372 111.227 110.461 47.131 45.799 43.955 41.602 14.521 14.829 14.965 15.160 15.283 15.737 15.752 15.773 15.448 15.935 15.937 15.285 15.736 15.742 15.752 15.936 16 4 246.809 243.909 243.176 242.991 69.950 68.724 68.232 68.029 75.398 74.140 73.635 73.425 50.316 50.570 50.764 50.870 14.368 14.352 14.345 14.343 15.618 15.613 15.612 15.611

319.781 356.983 368.346 377.480 107.475 152.707 159.642 163.925 89.037 164.994 172.017 174.690 67.757 157.493 173.423 88.094 164.649 170.667 172.045 172.175 51.119 49.895 48.786 47.086 21.102 21.827 22.084 22.375 23.211 24.328 24.366 24.414 23.636 24.836 24.842 23.214 24.326 24.342 24.365 24.840 25 5 246.809 243.910 243.176 242.991 100.984 99.165 98.436 98.134 116.012 114.066 113.283 112.958 50.316 50.570 50.764 50.870 20.742 20.709 20.695 20.690 24.030 24.021 24.017 24.016

388.559 435.688 465.781 504.639 139.164 200.594 210.056 214.981 123.691 234.348 244.478 248.465 95.054 226.090 248.988 122.397 233.848 242.467 244.511 247.185 62.113 60.896 61.690 62.948 27.323 28.671 29.059 29.343 32.245 34.554 34.630 34.725 33.158 35.654 35.666 32.253 34.550 34.583 34.627 35.661 36 6 248.850 246.991 246.524 246.407 129.818 127.424 126.463 126.064 163.836 161.053 159.935 159.471 50.732 51.209 51.463 51.585 26.665 26.610 26.588 26.578 33.936 33.916 33.908 33.905

478.443 535.783 582.431 651.190 162.497 237.152 248.566 253.227 161.172 313.478 327.260 332.860 125.431 306.595 337.691 159.508 312.794 324.432 327.290 335.229 76.481 74.886 77.140 81.228 31.905 33.897 34.386 34.564 42.015 46.222 46.356 46.520 43.754 48.349 48.373 42.032 46.214 46.274 46.350 48.364 49 7 250.833 248.743 248.218 248.087 150.737 147.863 146.713 146.238 217.674 213.915 212.408 211.783 51.136 51.572 51.816 51.936 30.962 30.878 30.845 30.832 45.088 45.048 45.033 45.027

696.381 851.228 1007.893 1106.376 1017.767 1277.229 1293.087 1295.630 199.921 400.647 418.579 426.082 158.038 398.709 439.215 197.867 399.751 414.783 418.596 435.987 111.320 118.976 133.491 138.007 199.828 182.557 178.882 176.844 52.117 59.075 59.291 59.548 55.128 62.875 62.915 52.140 59.061 59.161 59.281 62.900 64 8 253.564 251.508 250.992 250.863 959.592 952.139 950.177 949.677 276.002 271.161 269.220 268.417 51.693 52.145 52.395 52.518 197.104 198.834 199.766 200.222 57.170 57.104 57.078 57.068

766.306 930.457 1254.199 1439.666 1027.972 1304.205 1326.104 1331.648 238.235 493.580 516.082 525.745 192.104 502.074 553.181 235.820 492.443 511.178 516.074 549.076 122.498 130.049 166.113 179.581 201.832 186.413 183.449 181.760 62.105 72.778 73.102 73.477 67.011 79.175 79.240 62.140 72.756 72.909 73.085 79.215 81 9 337.235 332.179 330.654 330.157 959.592 952.139 950.177 949.677 336.966 330.967 328.563 327.569 68.750 68.871 69.025 69.118 197.104 198.834 199.766 200.222 69.797 69.698 69.659 69.644

890.920 1092.418 1677.158
1068.070 1393.716 1422.250 1432.226 274.559 589.334 616.709 628.727 226.653 616.269 679.138 271.805 587.934 610.581 616.660 674.045 142.418 152.687 222.132
209.704 199.207 196.750 195.488 71.574 86.896 87.356 87.870 79.063 97.184 97.283 71.623 86.864 87.087 87.330 97.245 100 10 389.324 382.371 380.228 379.513 970.250 963.501 961.797 961.369 398.337 391.162 388.285 387.094 79.370 79.277 79.374 79.450 199.293 201.207 202.209 202.687 82.510 82.375 82.321 82.299

1003.561 1266.292 1819.137
1121.065 1527.962 1568.308 1587.383 307.455 684.176 716.553 731.030 260.952 740.802 816.560 304.396 682.499 709.130 716.448 810.365 160.424 176.989 240.936
220.109 218.395 216.955 216.666 80.149 100.881 101.499 102.167 91.027 116.822 116.968 80.211 100.836 101.143 101.461 116.912 121 11 449.038 440.249 437.449 436.483 971.305 964.578 962.895 962.474 457.640 449.268 445.913 444.524 91.543 91.277 91.319 91.377 199.510 201.432 202.440 202.920 94.793 94.611 94.539 94.509

1557.709 1812.385

1175.215 1694.892 1751.443 1784.010 335.656 773.516 810.781 827.688 294.369 875.099 964.834 332.378 771.560 802.054 810.605 957.419 249.007 253.316

230.741 242.255 242.290 243.504 87.501 114.054 114.846 115.676 102.684 138.000 138.208 87.585 113.994 114.397 114.796 138.127 144 12 782.622 760.213 754.319 752.824 973.587 966.696 964.959 964.524 512.105 502.535 498.708 497.126 159.549 157.615 157.466 157.602 199.978 201.874 202.874 203.352 106.075 105.829 105.732 105.693

1561.255 1931.647

1220.465 1882.831 1958.367
358.389 851.985 893.700 912.842 326.301 1018.500 1123.252 354.918 849.767 883.758 893.449 1114.496 249.574 269.985

239.626 269.118 270.915
93.427 125.624 126.591 127.577 113.823 160.614 160.900 93.524 125.548 126.050 126.528 160.789 169 13 817.310 787.079 779.191 777.161 977.148 970.044 968.246 967.794 558.576 548.015 543.791 542.045 166.621 163.185 162.658 162.697 200.710 202.573 203.564 204.042 115.701 115.406 115.290 115.243

1608.660


1252.193


375.031 913.808 959.146 980.122 356.303 1170.244 1290.993 371.402 911.372 948.192 958.826 1280.776 257.152


245.855


97.765 134.740 135.862 136.980 124.288 184.544 184.929 97.868 134.650 135.241 135.786 184.778 196 14 884.992 851.631 843.276 841.121 982.108 974.799 972.955 972.492 594.214 582.929 578.409 576.538 180.419 176.568 176.036 176.087 201.729 203.566 204.554 205.032 123.083 122.759 122.630 122.576

1616.961


1270.474


385.025 953.571 1001.298 1023.492 384.206 1329.457 1467.118 381.364 950.989 989.668 1000.930 1455.315 258.479


249.444


100.371 140.603 141.833 143.041 134.022 209.651 210.158 100.493 140.503 141.156 141.749 209.959 225 15 931.268 900.120 892.271 890.247 987.564 980.415 978.615 978.163 616.898 605.004 600.254 598.291 189.853 186.622 186.264 186.372 202.849 204.739 205.745 206.228 127.781 127.408 127.261 127.201

1618.303


1277.740


1427.143


409.710 1495.142 1650.547 1425.511


1637.034 258.694


250.871


372.037


142.918 235.779 236.433 375.635


236.175 256 16 1022.576 984.632 974.972 972.543 991.919 985.129 983.418 982.989



208.468 204.144 203.528 203.600 203.744 205.723 206.754 207.245




1865.746


1592.815


1429.230


432.971 1666.162 1840.045 1427.493


1824.701 298.248


312.733


372.581


151.032 262.748 263.578 376.157


263.250 289 17 1022.620 984.636 974.973 972.544 1253.731 1237.690 1232.817 1231.219



208.477 204.144 203.528 203.600 257.521 258.466 259.188 259.580




1996.687


1610.143


1437.825


453.826 1841.225
1436.042



319.180


316.135


374.821


158.307 290.355
378.409



324 18 1023.447 995.768 988.646 986.841 1315.232 1297.342 1291.832 1290.003



208.645 206.452 206.383 206.593 270.153 270.923 271.595 271.974








1641.624


1452.086


472.532

1450.237







322.316


378.539


164.832

382.150



361 19 1042.893 1004.686 995.410 993.103 1407.013 1386.000 1379.452 1377.254



212.610 208.301 207.795 207.904 289.006 289.437 290.017 290.369








1689.362


1472.750


489.103

1470.701







331.689


383.926


170.613

387.542



400 20 1050.656 1012.066 1002.876 1000.611 1518.109 1493.410 1485.623 1482.974



214.192 209.831 209.353 209.476 311.825 311.867 312.338 312.658








1751.504


1500.282


503.710

1497.967







343.890


391.103


175.708

394.727



441 21 1269.022 1219.852 1206.751 1203.162 1636.329 1608.281 1599.289 1596.175



258.709 252.912 251.913 251.880 336.108 335.856 336.235 336.525








1818.223


1535.318


516.571

1532.667







356.989


400.236


180.194

403.871



484 22 1288.306 1235.661 1221.617 1217.694 1747.569 1716.437 1706.278 1702.698



262.641 256.189 255.016 254.922 358.957 358.442 358.729 358.983








1871.686


1578.626


527.762

1575.480







367.486


411.526


184.098

415.153



529 23 1304.295 1255.860 1242.652 1238.793 1833.745 1798.417 1786.867 1782.782



265.900 260.377 259.407 259.339 376.658 375.562 375.672 375.867












1630.678


537.315

1626.922











425.095


187.430

428.708



576 24 1855.667 1749.382 1712.980 1703.675







378.306 362.699 357.590 356.661
















1691.729


545.583

1687.201











441.010


190.314

444.592



625 25 1878.164 1749.398 1712.983 1703.676







382.892 362.702 357.590 356.661
















1761.543


552.515

1755.965











459.210


192.732

462.712



676 26 1883.733 1766.473 1743.511 1737.727







384.028 366.242 363.963 363.790
















1838.629


558.237

1831.784











479.305


194.728

482.691



729 27 1883.965 1785.448 1761.326 1755.233







384.075 370.176 367.682 367.455
















1919.939


562.760

1911.655











500.502


196.306

503.738



784 28 1909.401 1821.564 1798.312 1792.391







389.260 377.664 375.403 375.234




















566.286

1990.465















197.536

524.505



841 29
1948.299 1915.997 1907.606








403.940 399.970 399.354




















568.765


















198.401






900 30




































570.211


















198.905






961 31




































1466.956


















511.714






1024 32




































1469.178


















512.490






1089 33




































1476.822


















515.156






1156 34




































1489.636


















519.626






1225 35




































1507.811

































































1531.597

































































1561.234

































































1596.982

































































1639.058

































































1687.699

































































1742.770

































































1804.154

































































1871.536

































































1944.238