Tonight some light-hearted fun with generating function based animations
As with most of these posts I will just start with the results, which is this trippy animation:
Or check out this Dtube video:
The underlying equation
A single frame corresponds to a plot in the (x,y) plane of
for a fixed n. To generate the animation the frames are put together in ascending order where n starts from 0 and goes to 10 in tiny steps of 0.1.
Where does the trippiness come from?
At each frame the general description would be that you see hundreds of tiny circle like objects. So there are two things to explain:
Where do all these tiny circle like object come from? The equation x2+y2=1 corresponds to a circle. In the equation which generates the animation the equation for the circle is not really there but there is something like a variation present since the right hand side has the term sin(nx)2 + sin(ny)2. Since the left hand side of the equation is always positive this generates circle like objects.
Why are there so many of these disconnected things? If you would draw sin(x)2= 1/10 then you would get a lot of disconnected points since the sinus is periodic. Three sinuses appear in the equation for the animation, so that's why you get all these disconnected components.
Let's go to 3D
The equation has three variables: x,y,n. Consequently, we can represent it in 3D where the axes are given by x,y,n. This gives something which looks like it could be a puzzle box from a horror movie:
Unfortunately, it is so messy that you don't get a good idea of what's going on. So for this case it is more clear to present a 3D equation in 2D.
Conclusion and steemit basic income giveaway!
s do,[;r rwisyopm vsm hrmrtsr vtsxu djoy
1 steemitbasicincome for the first to translate this message :D
Sources: Equation made using quicklatex it is free!
Merchandise :D
There is a MathOwl shop which sells my artsy fartsy stuff. If you got some spare money head over there. You can learn about the colors of pi over here here. I also have really cheap stuff available like these stickers They are an absolute hoot.
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