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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"A single equation can generae [sic] crazy shit."
well nice job in finding the error. Sent you a 0.5 Steem reward in the form of dustsweepervote. Learn more here-> https://steemit.com/dustsweeper/@dustsweeper/dustsweeper-faq
Hey, that's nice, thanks a lot!
a simple equation can generate crazy shit
s do,[;r rwisyopm vsm hrmrtsr vtsxu djoy
Letter substitution by sliding keys one to the right, very simple cipher, I enjoyed it however. <3
good job :) sent the share
Oh damn, my phone didn't show the first comment. Oh well.
sexy maths!! I love it!
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The Creative Crypto is all about art on the blockchain and learning from creatives like you. Looking forward to crossing paths again soon. Steem on!Hello @mathowl, thank you for sharing this creative work! We just stopped by to say that you've been upvoted by the @creativecrypto magazine.