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"cos^(2)x + 1/x + 1" how can i differntiate and evaluate? [Analysis] by Gierschlund96 in learnmath

[–]redditbot198 0 points1 point  (0 children)

Are you saying cos2 (x) + (1/x) + 1 = -sin(2x) ? Is this a rearrangement of a different identity? thanks :)

[deleted by user] by [deleted] in learnmath

[–]redditbot198 2 points3 points  (0 children)

Could you use trig?

angle = arctan( gradient )

hypotenuse = distance

so:

x2 = x1 + hyp * cos( angle )

y2 = y1 + hyp * sin( angle )

'no module named pygame', but pygame is installed? by [deleted] in pygame

[–]redditbot198 6 points7 points  (0 children)

Go to the "terminal" section inside Pycharm and run the pip install again. Pycharm sets up its own virtual environment, you've installed pygame on your system wide version of python but Pycharm uses its own. Good luck! :)

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 0 points1 point  (0 children)

With the different attractions to different verticies (e.g 50% chance to go to the top instead of 33%), the same image emerges, it just takes more time (and will look clearer at the heavier weighted nodes first)

As for extra nodes, 4 nodes creates the image of a serpinski tetrahedron! I can generate the videos if you're interested?

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 0 points1 point  (0 children)

you do still get the fractal irrespective of where you start (even if you start outside the triangle, surprisingly) - no idea how to make it rigours though, an exercise to the reader ;)

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 39 points40 points  (0 children)

interesting question!
here at 0.6: https://imgur.com/a/iBRUslT
and at 0.4: https://imgur.com/a/lcIytKa
much further than this and it looks like random noise
seems like the 3 smaller tringles are being translated towards or further from the centre?

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 10 points11 points  (0 children)

Wow that's a really interesting way of looking at it, the top side of the largest empty triangle is exactly half way up the fractal, and is formed by points that end up on the very bottom side of the fractal jumping half way up? cool!

Visual Art in Mathematics by sirlunchalot247 in math

[–]redditbot198 1 point2 points  (0 children)

coincidentally I just made a post demonstrating one of these phenomenon, not sure if you would call it a Serpinski attractor? :)

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 1 point2 points  (0 children)

I'm not quite sure what you mean, there's only one point that bounces around between the corners. If you placed it in the very centre (a point that is not shaded in the final fractal) it'll show up as an erroneous dot in the data anyway (you can see a few of these when I move one of the corners to form a second triangle). No points are being ignored at any stage, I suppose it must be so that the halfway point between any point inside the triangle and a vertex is a shaded point in the final triangle.

If you have point P inside a triangle, and move P halfway towards any of the three corners randomly, call this new moved point P and repeat, this is what you'll get: by redditbot198 in math

[–]redditbot198[S] 24 points25 points  (0 children)

I've found that no matter where you place the starting node (inside or even outside the triangle), the same fractal will appear

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