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u(t) is called 60 times per second. t: Elapsed time in seconds. S: Shorthand for Math.sin. C: Shorthand for Math.cos. T: Shorthand for Math.tan. R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5) c: A 1920x1080 canvas. x: A 2D context for that canvas.
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  • We can get a lot more decimals with Ramanujan, but I couldn't make it fit in a 140bytes
  • u/donbright
    c.width|=M=Math;(26390*n+1103)/M.pow(396,4)
  • u/donbright
    oops sorry wrong textarea!!!!
  • u/donbright
    so uhh looks like Ramanujan maxes out the JS floating point type after about n=4
  • u/donbright
    unless u calc pi using an 'nth digit' formula i guess.......
  • u/Pyrofoux
    Yep, that's what I meant by "more decimals" :)

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  • Old school plasma effect

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  • As with 1857 this is an attempt to show the relation between Binary Quadratic Forms and the Circles and Squares pseudo fractal and Moiré pattern. This takes the basic ingredients of the Quadratic Form, x*x, y*y, and 2*x*y, and mixes them together, but slowly varies the amount of each ingredient over time with the Sine function. It is possible to see how all variations of the Quadratic Form result in similar patterns, transitioning from crcles to ovals to hyperbola patterns. Inspiration from this site and NJ Wildberger's rational geometr, Paul Bourke's http://paulbourke.net/fractals/circlesquares/ and Santiago Zubeta

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remix of d/479 by u/lionleaf

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  • A transition from x*x+y*y (the Blue geometry, circles) to x*x-y*y (the Red geometry, hyperbolas). This shows a linkage between Binary Quadratic Forms and the Circles and Squares pseudo Fractal / Moiré pattern. By transitioning between two different Binary Quadratic Forms slowly, I hoped to show that the forms themselves are what form these patterns, not simply circles or hyperbolas or trig functions. Inspiration from many dweets on this site and Wildberger's Chromogeometry.
  • u/donbright
    Binary Quadratic Forms are where you take any combination of x*x, y*y, and 2*x*y, for example 3*x*x+2*y*y (an ellipse), of x*x-y*y/2 (a squished hyperbola)

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  • Show more comments…
  • u/FireFly
    I would love an explanation or pointer about the maths going on here… in particular I don't understand why the 1.56 constant for the b= is so sensitive. It looks like an approximation of π/2, but all of π/2, 1.57 and 1.5 behave vastly differently/more chaotically. So what's the relationship between these numbers/how is 1.56 derived?
  • u/tapgiles
    What the... @.@ Looks so detailed!
  • u/joeytwiddle
    Some other constants with similar behaviour: 1.17, 2.34, 3.12, 3.51, 3.90, 4.68, 6.24
  • u/joeytwiddle
    And a few with different behaviour: 3.08, 6.05 (!), 6.35

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dh7

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  • u/iverjo
    Nice halftone smoke. This technique deserves more attention, in my opinion

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