room topic changed to Primes and Squares: For discussion about programming, math, and science, and related topics. Not about PPCG (the site itself) or golfing. (no tags)
So... I have an object with a known initial velocity and known acceleration. How do I solve for its trajectory when the magnitude of acceleration is constant and is at a fixed angle relative to velocity?
When angle = 0 or 180, it's linear acceleration, when angle = 90 it's circular motion.
@PhiNotPi that seems to be a differential equation. Let x be the position, v = x' be the velocity, and a = v' = x'' be the acceleration. you want the angle (i.e. the scalar product) between v and a to be constant, that means (v/||v|| , a/||a||) = (x'/||x'|| , x''/||x''||) = const. This does not seem to be trivial to solve. And I'm not sure whether a logarithmic spiral actually solves this. (there the angle between the velocity and the origin is constant)
(here x(t) is a vector and (...,...) a scalar product)
In what ways do the points from the gist actually differ from the points you posted above? Can't you apply the same method you used for the gist points here too?
The first two blocks are simulations of the 1st and 2nd harmonic, respectively. They are pretty much perfect. The third is the sum of those two harmonics, and there are some errors in it.
For each point on the string, I calculate its current velocity and current acceleration (I'm referring to the trajectory of a complex number on the complex plane).
Now, the problem is that, when I discretize a cosine wave, the values for acceleration/velocity for the individual points don't match up with what the values should be.
for example, halving the wavelength should quadruple the velocity, but it doesn't when you calculate it using discrete points.
for example, the wave (0,1/sqrt(2),1,1/sqrt(2),0) should have twice the velocity of (0,1,0)
But here, the velocities are actually calculated to be 1/sqrt(2)-1 = -29289 and 0-1 = -1 repsectively
so I basically had to write an equation that relates the calculated velocity to the real velocity
@El'endiaStarman First wave has wavelength 8 and second has wavelength 4.
I perform v^2/a to determine which point the complex number is rotating around, and then perform a bunch of corrections to figure out how fast the complex number is rotating.
it's really a mess
I need to leave now... I might be back in an hour or so?
btw: I was recently looking for a way to parametrize the mandelbrot set. And Perhaps this migth lead to something, as the first big "blob" contains a cardioid!
(I though a parametrization would be nice for drawing buddhabrot images, as we there need the points that diverge, but do so very slowly. These are the points that are very close to the border of the set.)
IIRC the Mandelbrot set is connected, meaning that all points within the set can be reached from another point in the set by passing through points within the set.
Which I suppose does mean that it has a border, but still, seems like it'd be really hard to figure out a parameterization.
Does anyone know how to parametrize the boundary of the Mandelbrot set? I am not a fractal-geometer or a dynamical systems person. I just have some idle curiosity about this question.
The Mandelbrot set is customarily defined as the set $M$ of all points $c\in\mathbb{C}$ such that the iterates...
hey, I'm considering having "states" for classes. A good example is a File class: It can have the "unopened", "opened", and "closed" states. Certain methods could be defined as unavailable/available under certain states, which would require a check for that state unless the compiler can deduce the state
Do you mean drawing a curved line or a straight? The latter is the easier of the two.
I'm basically drawing a point at each circle's centre at every frame. But by increasing the width of the points, the overall pattern looks more like a line
All I need to do is to store the positions into an array (length 2 to keep it simple), and draw a line from the current pos to the previous pos while updating the array with the newer positions.
Looking at this chatroom as an experiment, I'd say that it has been going well. I'm finding the conversation here more interesting and more worthwhile than on TNB
Even though I haven't found time to participate yet, I have been following the conversation and I agree. It will be interesting to see how this room develops as more people become aware of it.
I definitely like this room a lot more than TNB right now. I feel like this room is, in a way, like what TNB used to be. A year ago, there was definitely a lot more "noise", but at the same time, users were better at prioritizing interesting conversations.
At least you didn't have to suffer through Nathan making you figure it out. ;)
It used to be "Nonsquare rectangles on an n X n board" and then "1100101110110101". The latter is 52149 in binary, and the former is the title of OEIS sequence A052149.
@quartata @El'endiaStarman Traits (I said attributes earlier mistakenly) are declared with a variety of "proofs", and can also be attached to a variable type or a return type.
So, for example, the trait "positive" has a proof of "T>0"
If you make that check, or the exact value is known, and it passes that check, then you know that trait at compile time
For my earlier example, the proof of a file being in the open state is either calling the method open() or can be checked via isOpen()
Alternatively, you could also have a function that returns a File[FileState=Open]
I awoke with the following puzzle and I would like to investigate but the answer may require some programming (it may not either). I have asked on the meta site and believe the question to be suitable and hopefully interesting for the community.
I will try to explain the puzzle as best I can th...
@PhiNotPi I was about to suggest to ATaco that they do the path-drawing part but with random odd numbers when I realized that the spacing between primes is responsible for this pattern, so it's not really that easy to specify a random distribution that has approximately the same distribution.
I think an even better option is to auto-scale when the line wanders over a fairly significant region of space. I.e. the extremes are more than 1 pixel apart or whatever.
I think I have to eat some chocolate to compensate for my guilt of cheating.
It feels like a living thing...
@El'endiaStarman It is just such an easy thing to do with complex numbers: Just divide every intermediate one by the very last.
I wonder if there is such a thing as a maximal displacement, or if such a sequence stays bounded within a certain area for all upper bounds and all angles.
Each time it reaches a new most distance point, and then returns close to the origin, the image will be magnified as it approaches the origin and make the most distant point a new outer bound
Oh...you're basically asking if there's a maximum ratio between the greatest displacement from the origin and the displacement between the start and end points?
Does anyone know how to parametrize the boundary of the Mandelbrot set? I am not a fractal-geometer or a dynamical systems person. I just have some idle curiosity about this question.
The Mandelbrot set is customarily defined as the set $M$ of all points $c\in\mathbb{C}$ such that the iterates...
