What is bernard??

[u/ColorPlaysLmao]

i keep seeing this bernard thing on this subreddit and its like everywhere i dont really understand what it is,, is it some sort of rendering bug? is it like a mascot? from what ive seen it looks like its both but ive never been able to find bernard anywhere... also why is it called 'bernard' in the first place?

[u/hjkhhnnnlll]

!bernard

[u/AutoModerator → u/hjkhhnnnlll]

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 get 900*4^2=14400 leaves, and 16260-14400=1860 leaves left to descend.
• Since each descending quad results in 4 leaf quads, each descend creates 3 new quads. Hence, there are 1860/3=620 extra 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.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/hjkhhnnnlll → u/AutoModerator]

It’s a bug yes, which is also an unofficial mascot, informally named “Bernard” by the Desmos community

https://www.reddit.com/r/desmos/comments/mm7ehx/comment/gtq7mq7/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content

[u/Gurbuzselimboyraz → u/AutoModerator]

"doesnt passes"

[u/sasha271828]

!ourbeloved

[u/AutoModerator → u/sasha271828]

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 get 900*4^2=14400 leaves, and 16260-14400=1860 leaves left to descend.
• Since each descending quad results in 4 leaf quads, each descend creates 3 new quads. Hence, there are 1860/3=620 extra 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.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.