Talk:Harmonograph

Category
Just wondering, what would be a good category for this article? Oleg Alexandrov 03:41, 7 Mar 2005 (UTC)


 * What about 'Writing instruments?' Although it does "produce a smooth, controllable line," it also does the controlling of the line too, so would that be appropriate? Perhaps 'Art media?' 12.218.76.10 (talk) 23:47, 23 October 2011 (UTC)

Merge proposal
Can we merge Blackburn Pendulum into the Harmonograph article then make it a redirect? (Seems to me that it's just a different name for the same thing.) 12.218.76.10 (talk) 23:15, 23 October 2011 (UTC)
 * The Blackburn pendulum seems to be a special case of a Harmonograph. RJFJR (talk) 21:13, 5 March 2012 (UTC)

Variable ranges?
What are the ranges for the variables in the equations? SharkD  Talk  03:00, 26 August 2013 (UTC)


 * Any range you want. They will just look progressively stupider.
 * $$x(t) = A \sin (tf + p) e^{-dt}, \,\!$$
 * The equations given are just for any generic figure which is created by the motion of four pendulums. You can actually mix and match them all you want. The amplitude is basically a scaling factor of that particular pendulum. The sum of the pendulums amplitudes in a particular dimension is the max distance of that dimension. The frequency (f) can be anything it's how many times it goes back and forth per unit of time. 0 would be particularly dotlike, -frequencies wouldn't cause any issues. The phase will be modded by 2Pi because it's tossed into a sin wave (the cos waves for the other bits could just be sin waves with a phase, so you could just use all sins or cos's). The damping is the one that'll screw you. 0 is fine, but you have to arbitrarily truncate the drawing process. Negative damping causes it to make harmonographs that get progressively bigger and therefore look exactly like big harmonographs that get progressively smaller. And if the damping is too high it will prematurely die off. So you're thinking like 0.01-ish. In an actual harmonograph it's basically the friction. Tat (talk) 23:18, 29 May 2015 (UTC)

Pintograph equation
What are the equations for the pintograph? Thanks. SharkD  Talk  05:15, 26 August 2013 (UTC)


 * The way those arms works means that the angle of the arm is going to be the result of the relative positions of the attachment points. And the radius of the arm is the product of the closeness of the two points. You have two points on two circles of varying sizes rotating at varying speed. The drawing point would be calculated as a polar coord from the midpoint of the two points, perpendicularly at a radius relative to the distance of the two points.

Off the top of my head.


 * x = m1 + cos(theta)*r
 * y = m2 + sin(theta)*r
 * theta = atan(y1-y2,x1-x2) + 90°
 * r = S sqrt((x1-x2)²+(y1-y2)²)
 * x1 = h1 + r1 * cos(theta1)
 * y1 = k1 + r1 * sin(theta1)
 * x2 = (h2 + r2 * cos(theta2))
 * y2 = (k2 + r2 * sin(theta2))

m1 = (x2 - x1) / 2 m2 = (y2 - y1) / 2
 * theta1 = v1 * t;
 * theta2 = v2 * t;

Where,
 * v1 is the speed of the first wheel.
 * v2 is the speed of the second wheel.
 * S is a static scaling factor
 * h1 is the x position of the center of the first wheel.
 * k1 is the y position of the center of the first wheel.
 * h2 is the x position of the center of the second wheel.
 * k2 is the y position of the center of the second wheel.


 * It does assume the arms are the same length. They don't have to be. You could picture them as static length arms attached to a triangle and solve for the location of the pointer from that position. Given that you have all three sides, it wouldn't be hard to solve for the location of point C. Though you could just jitter the already given harmonograph math and say that you have two (two axis) pendulums with no damping at all, traveling in circles.

Tat (talk) 08:49, 28 May 2015 (UTC)

Removed dead link
The previous link to "Online Interactive Harmonograph" {http://www.sequences.org.uk/harmonograph) was dead. I replaced the link without realizing that my replacement was already in the list of external links. Oops. It's now deleted, and is as it should be.Twistlethrop (talk) 03:45, 4 September 2014 (UTC)

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