[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8},"actionData","errors","root",{"_26":27,"_28":29,"_30":12,"_31":12,"_32":12,"_33":12,"_34":12,"_35":12,"_36":37},"routes/canvas.shared.$sharedTextdocId",{"_9":10,"_11":12},"sharedTextdoc",{"_13":14,"_15":-7,"_16":17,"_18":19,"_20":21,"_22":23,"_24":12,"_25":12},"isAuthenticated",false,"sharedTextdocId","6a15da73c5b08191a2dc34c3ac6ceca6","versionInt","title","Simplified Unit Distance Visualizer","type","code/html","content","\n\n\n \n \n A simpler picture of a unit-distance construction\n \n\n\n

A simpler picture of a new unit-distance construction

\n This interactive diagram is a small, simplified model of what the new construction could look like.\n It starts with a highly structured grid in four dimensions, keeps only the points that pass a hidden\n “window” test, and then projects the surviving points down to the plane. The result is a dense patch\n with many pairs of points exactly one unit apart.\n

\n\n

\n Window size R \n \n

\n\n

\n Search range B \n \n

\n\n

\n Point size \n \n

\n\n

\n Zoom \n \n

\n\n

\n show unit-distance lines\n highlight points away from the boundary\n show the 12 one-unit directions around the origin\n crop the visible picture to the same window size\n

\n\n

0points drawn

0unit edges drawn

0inner points

4grid dimensions

\n\n \n\n

\n This is not the full mathematical construction that improves the asymptotic bound.\n It is a smaller, drawable version of the same broad idea: build a richer grid than the ordinary\n square lattice, use a hidden filter to choose a finite set of points, and then project those points\n into two dimensions.\n

\n When the line overlay is turned on, each segment connects two points that are exactly one unit apart\n in the displayed plane. Increasing R keeps a larger patch of the construction. Increasing\n B only expands the computer search; once it is large enough, raising it should no longer\n change the counts.\n

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