Cantor's function

Visit http://tube.geogebra.org and search for "Cantor." When you find an applet you like, click "Created with GeoGebra at the bottom", then click "Download" and "Download GeoGebra file". When you open the file in GeoGebra, you can "View" . . . "Construction Protocol" or "Algebra View" to see how it's done.

Here's one way to do it: In the Input bar, try these three commands:

1) n = slider[1, 10, 1]

2) f(x) = 0, (or anything, really)

2) list1 = {1, 7, 19, 25, 55, 61, 73, 79, 163, 169, 181, 187, 217, 223, 235, 241, 487, 493, 505, 511, 541, 547, 559, 565, 649, 655, 667, 673, 703, 709, 721, 727, 1459, 1465, 1477, 1483, 1513, 1519, 1531, 1537, 1621, 1627, 1639, 1645, 1675, 1681, 1693, 1699, 1945, 1951, 1963, 1969, 1999, 2005, 2017, 2023, 2107, 2113, 2125, 2131, 2161, 2167, 2179, 2185, 4375, 4381, 4393, 4399, 4429, 4435, 4447, 4453, 4537, 4543, 4555, 4561, 4591, 4597, 4609, 4615, 4861, 4867, 4879, 4885, 4915, 4921, 4933, 4939, 5023, 5029, 5041, 5047, 5077, 5083, 5095, 5101, 5833, 5839, 5851, 5857, 5887, 5893, 5905, 5911, 5995, 6001, 6013, 6019, 6049, 6055, 6067, 6073, 6319, 6325, 6337, 6343, 6373, 6379, 6391, 6397, 6481, 6487, 6499, 6505, 6535, 6541, 6553, 6559, 13123, 13129, 13141, 13147, 13177, 13183, 13195, 13201, 13285, 13291, 13303, 13309, 13339, 13345, 13357, 13363, 13609, 13615, 13627, 13633, 13663, 13669, 13681, 13687, 13771, 13777, 13789, 13795, 13825, 13831, 13843, 13849, 14581, 14587, 14599, 14605, 14635, 14641, 14653, 14659, 14743, 14749, 14761, 14767, 14797, 14803, 14815, 14821, 15067, 15073, 15085, 15091, 15121, 15127, 15139, 15145, 15229, 15235, 15247, 15253, 15283, 15289, 15301, 15307, 17497, 17503, 17515, 17521, 17551, 17557, 17569, 17575, 17659, 17665, 17677, 17683, 17713, 17719, 17731, 17737, 17983, 17989, 18001, 18007, 18037, 18043, 18055, 18061, 18145, 18151, 18163, 18169, 18199, 18205, 18217, 18223, 18955, 18961, 18973, 18979, 19009, 19015, 19027, 19033, 19117, 19123, 19135, 19141, 19171, 19177, 19189, 19195, 19441, 19447, 19459, 19465, 19495, 19501, 19513, 19519, 19603, 19609, 19621, 19627, 19657, 19663, 19675, 19681, 39367, 39373, 39385, 39391, 39421, 39427, 39439, 39445, 39529, 39535, 39547, 39553, 39583, 39589, 39601, 39607, 39853, 39859, 39871, 39877, 39907, 39913, 39925, 39931, 40015, 40021, 40033, 40039, 40069, 40075, 40087, 40093, 40825, 40831, 40843, 40849, 40879, 40885, 40897, 40903, 40987, 40993, 41005, 41011, 41041, 41047, 41059, 41065, 41311, 41317, 41329, 41335, 41365, 41371, 41383, 41389, 41473, 41479, 41491, 41497, 41527, 41533, 41545, 41551, 43741, 43747, 43759, 43765, 43795, 43801, 43813, 43819, 43903, 43909, 43921, 43927, 43957, 43963, 43975, 43981, 44227, 44233, 44245, 44251, 44281, 44287, 44299, 44305, 44389, 44395, 44407, 44413, 44443, 44449, 44461, 44467, 45199, 45205, 45217, 45223, 45253, 45259, 45271, 45277, 45361, 45367, 45379, 45385, 45415, 45421, 45433, 45439, 45685, 45691, 45703, 45709, 45739, 45745, 45757, 45763, 45847, 45853, 45865, 45871, 45901, 45907, 45919, 45925, 52489, 52495, 52507, 52513, 52543, 52549, 52561, 52567, 52651, 52657, 52669, 52675, 52705, 52711, 52723, 52729, 52975, 52981, 52993, 52999, 53029, 53035, 53047, 53053, 53137, 53143, 53155, 53161, 53191, 53197, 53209, 53215, 53947, 53953, 53965, 53971, 54001, 54007, 54019, 54025, 54109, 54115, 54127, 54133, 54163, 54169, 54181, 54187, 54433, 54439, 54451, 54457, 54487, 54493, 54505, 54511, 54595, 54601, 54613, 54619, 54649, 54655, 54667, 54673, 56863, 56869, 56881, 56887, 56917, 56923, 56935, 56941, 57025, 57031, 57043, 57049, 57079, 57085, 57097, 57103, 57349, 57355, 57367, 57373, 57403, 57409, 57421, 57427, 57511, 57517, 57529, 57535, 57565, 57571, 57583, 57589, 58321, 58327, 58339, 58345, 58375, 58381, 58393, 58399, 58483, 58489, 58501, 58507, 58537, 58543, 58555, 58561, 58807, 58813, 58825, 58831, 58861, 58867, 58879, 58885, 58969, 58975, 58987, 58993, 59023, 59029, 59041, 59047}

3) For the slider 'n', under "Object Properties", "Scripting", "On Update", paste this:

execute[{Sum[join[{"SetValue[f,"}, join[Sequence[Sequence["If[" + Element[list1, t]/3^w + "<x<" + (Element[list1, t]+1)/3^w + ", " + (2*t-1)/2^w +", ", t, 1, 2^(w-1)], w, 1, n]], {"0]"}, Sequence["]", t, 1, 2^n-1]]]}]

Edit: Now f is a function and list1 is half its original size.

Hi, another way with the recursive spirit but only a polyline and not a function.

A way to have the list of the points recursively : (checked with n<=13 on my old computer)

Execute[Sequence["SetValue[list1,RemoveUndefined[Join[Sequence[If[y(Element[list1, k]) ≠ y(Element[list1, k + 1]), {Element[list1, k], (x((2 (Element[list1, k]) + Element[list1, k + 1]) / 3), y((Element[list1, k + 1] + Element[list1, k]) / 2)), (x((Element[list1, k] + 2 (Element[list1, k + 1])) / 3), y((Element[list1, k + 1] + Element[list1, k]) / 2)),Element[list1, k + 1]}], k, 1, Length[list1]-1]]]]",k,1,n]]

https://ggbm.at/569009

Tried as a real function (with n<=9 at home)

https://ggbm.at/569013