Mark McClure
Reputation
25,084
200/100 score
 22h comment Can Mathematica produce manipulatable 3D plots for deployment on the web? @EmilioPisanty Very nice! I almost feel silly for answering the question now. :) Jan 18 comment How does Mathematica calculate $\sin(\pi/5)$? @Szabolcs I don't think you need to be a developer to guess that it works by a simple lookup. Jan 18 comment Using Solve to solve the equation $x^{1/3}=-1$ I don't think there is a solution. I believe that the image of the complex plane under $z\to z^{1/3}$ is $\{r e^{i\theta}: r\geq 0, -\pi/3 < \theta \leq \pi/3\}$, given the location of the branch cut. Dec 24 comment Revolution of Koch Snowflake @ubpdqn Thanks - and same to you! Dec 11 comment Numerically evaluating an integral related to Cantor's staircase @J.M. Glad you like it! Dec 7 comment Basins of attraction of equilibrium points For the system $x'=V_x,y'=V_y$, an equilibrium will be attractive iff it's a local minimum of the potential function. Before proceeding further, though, you should make sure that's the system you're interested in. Perhaps, you're really interested in a second order system, which is likely in celestial mechanics. That's a more complicated question, as you've got to deal with initial conditions on $x'$ and $y'$ as well. Dec 7 comment Basins of attraction of equilibrium points As you have shown, the algebraic system $V_x=0,V_y=0$ has four numeric solutions and, if we apply Newton's method to that system, each of those solutions has an interesting basin of attraction. But that is a different question from whether those equilibrium points are attractive under a system of differential equations like $x'=V_x,y'=V_y$. Dec 7 comment Basins of attraction using Newton's method Part II I agree with Quantum_Oli - it would be nice to know where this came from. It appears there might be an interesting question here but the image looks like the Julia set of a polynomial - I can't imagine how your non-differentiable function generated it. Dec 7 comment Basins of attraction of equilibrium points I'm quite sure that the basins of attraction of Newton's method in two real variables have been well studied; there's an elementary discussion on pages 486-487 of Gil Strang's calculus text. If you're interested in studying the basins of attraction of the smooth dynamical system with a given potential, however, that's quite a different thing. Only one of your equilibrium points is attractive for that system. Dec 5 comment Basins of attraction using Newton's method The first thing my answer to that question does is generalize the code to arbitrary functions. I guess that's what @Saurav is referring to. Nov 11 comment Can Mathematica Handle Open Intervals? Interval complements? @alancalvitti True - but, again, I don't think it's hard to roll your own depending on your needs. Nov 11 comment Can Mathematica Handle Open Intervals? Interval complements? @alancalvitti There is no such function that I know of, though it should be quite easy to create one using patterns. Something like `toInequality[Interval[{a_,b_}], var_] := a