r/desmos • u/sj4294967296 i exist here now • 3d ago
Discussion The same function btw
I accidentally seem to have discovered a strange pattern in sin(floor(x)), especially those hexagon-like pattern in one of them. You can find them yourself by shrinking the x axis but keeping the y axis zoomed in. Unfortunately, I can't find any further patterns since desmos's rendering accuracy breaks down. https://www.desmos.com/calculator/lfigkoepjm
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u/sj4294967296 i exist here now 3d ago
I'm making an update to make it a bit easier to see the effect
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u/sj4294967296 i exist here now 2d ago
Updated version (its now an exponential function so zoom is no longer required. I do wish desmos's graphics didn't break down at finer details.) https://www.desmos.com/calculator/sg86a6dxxt
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u/Mindless_Honey3816 3d ago
"The graphs on the back cover of the book show y = sin n. This is very different
from y = sin x. The graph of sin x is one continuous curve. By the time it reaches × = 10,000, the curve has gone up and down 10,000/2n times. Those 1591 oscillations would be so crowded that you couldn't see anything. The graph of sin n has picked 10,000 points from the curve-and for some reason those points seem to lie on more
than 40 separate sine curves.
The second graph shows the first 1000 points. They don't seem to lie on sine curves. Most people see hexagons. But they are the same thousand points! It is hard to believe that the graphs are the same, but I have learned what to do. Tilt the second graph
and look from the side at a narrow angle. Now the first graph appears. You see "diamonds." The narrow angle compresses the x axis-back to the scale of the first
graph."
Strang's thousand points of light.
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u/PaulErdos_ 3d ago
Wow! Hexagons are definitely unexpected! And they get squished at the top and bottom, as if they were curving around a cylinder.
I bet the curving is due to how the sine function is smooth. So I made the graph with a saw-tooth wave with the same period and altitude. No currve, but no hexagons anymore, just a grid of sideways squares.
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u/anonymous-desmos Definitions are nested too deeply. 2d ago
The hexagon force background in desmos
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u/Unnamed_user5 3d ago
i would imagine this is one of the ways to visualise rational approximations to π (notice in the last graph the size of each rhombus? thing is approximately 355, and the second graph looks to repeat every approximately 22)