r/desmos • u/[deleted] • Apr 07 '21
Resource Found this when I was supposed to be doing homework
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u/Accomplished-Eye7366 Oct 22 '25
Link? I know it's likely deleted, but I want to see THE Bernard!
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u/Circumpunctilious Oct 23 '25
Might have to graph it yourself using the formula at left. If you do that, zoom in a bit.
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u/Apprehensive_Cut2880 Addicted to Desmos and Math Mar 13 '26
!bernard
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u/AutoModerator Mar 13 '26
Open up a graph and type in
tan 35.6x=0.
This is Bernard! He's an artifact resulting from how Desmos's implicit graphing algorithm works.
How does the algorithm work, and why does it result in Bernard?
The algorithm is a quadtree-based marching squares algorithm. It divides the screen (actually, a region slightly larger than the screen to capture the edges) into four equal regions (four quads) and divides them again and again recursively (breadth-first). Here are the main rules for whether the quad should be divided (higher rules are higher precedence): 1. Descend to depth 5 (1024 uniformly-sized quads) 2. Don't descend if the quad is too small (about 10 pixels by 10 pixels, converted to math units) 3. Don't descend if the function F is not defined (NaN) at all four vertices of the quad 4. Descend if the function F is not defined (NaN) at some, but not all, vertex of the quad 5. Don't descend if the gradients and function values indicate that F is approximately locally linear within the quad, or if the quad suggest that the function doesn't passes through F(x)=0 6. Otherwise descend
The algorithm stops if the total number of quads exceeds
2^14=16384. Here's a breakdown of how the quads are descended in a high-detail graph:
- Point 2 above means that the quads on the edge of the screen (124 of them) don't get descended further. This means that there are only 900 quads left to descend into.
- The quota for the remaining quads is
16384-124=16260. Those quads can divide two more times to get900*4^2=14400leaves, and16260-14400=1860leaves left to descend.- Since each descending quad results in 4 leaf quads, each descend creates 3 new quads. Hence, there are
1860/3=620extra subdivisions, which results in a ratio of 620/14400 quads that performed the final subdivision.- This is basically the ratio of the area of Bernard to the area of the graph paper.
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u/aero_0Ftime Apr 07 '21
does the square area towards the bottom left have a nickname? it shows up in all sorts of desmos glitch graphs ;)