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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
February 6, 2022
Question

Portrait of roots of two equations

  • February 6, 2022
  • 7 replies
  • 22019 views

I announce a competition - who will create the most interesting and beautiful portrait of the roots of two equations. I will send a hard copy of my book (2⁵ Problems for STEM Education - 1st Edition - Valery Ochkov - Rout (routledge.com)) to the winner of the contest. The end date of the competition is April 1, 2022. I will personally determine the winner. Materials explaining the essence of the task, in attachment. In the picture - a sample of a work of science and art, which should be submitted to the competition.

8-Portret.png

    7 replies

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    February 7, 2022

    Portrait not Find but Minimize function. f(x, y) is Himmelblau's function - Wikipedia

    14-Portret-Minimize.png

    W
    Werner_E25-Diamond I
    25-Diamond I
    February 8, 2022

    It looks like the for points in your picture (the right one) are not placed at their correct corresponding position as they are not collinear. You may compare with the pic below:

    Werner_E_0-1644293957642.png

    It may also be interesting to zoom in at specific positions. As far as I tried its chaotic but by far not as nice as doing it with the Mandelbrot.

    Werner_E_1-1644296525860.png

    Werner_E_0-1644297568272.pngWerner_E_1-1644298982531.png

     

     

     

     

      V
      24-Ruby IV
      ValeryOchkov24-Ruby IVAuthor
      24-Ruby IV
      February 8, 2022

      Thanks, Werner! You have as we say in Russian "глаз-алмаз".

      AB.png

      9-Portret.png

      W
      Werner_E25-Diamond I
      25-Diamond I
      February 8, 2022
      @ValeryOchkov wrote:

      Thanks, Werner! You have as we say in Russian "глаз-алмаз".

      Oh, yes! I am so sharp-eyed that sometimes I even see things that aren't there - but that's another story 🙂

       

      I think it's better to have the points automatically entered into the image than to do it afterwards with an image editor.

       

      Do you remember that one specific regular contributor in this forum always used to say that "a solution without an animation isn't a solution" ?

      Ani2.gif

      W
      Werner_E25-Diamond I
      25-Diamond I
      February 8, 2022

      OK, think I have played around enough for now.

      Here is a last animation showing symmetrical pictures (slope of line is zero). Its interesting to see that sudden appearance of the many black areas (no solution found) when the intercept gets positive.

      Werner_E_0-1644329268845.pngWerner_E_1-1644329304434.png

      ani3.gif

        V
        24-Ruby IV
        ValeryOchkov24-Ruby IVAuthor
        24-Ruby IV
        February 8, 2022

        Yes, it's time to finish! And then at night such a terrible muzzle dream. Some kind of mysticism begins.

        See Medusa - Wikipedia

        BH.png

         

        W
        Werner_E25-Diamond I
        25-Diamond I
        February 8, 2022
        @ValeryOchkov wrote:

        Yes, it's time to finish! And then at night such a terrible muzzle dream. Some kind of mysticism begins.

        See Medusa - Wikipedia

         

        I was rathetr thinking more of a demon. And he doesn't have to keep you awake if you penetrate his brain. Not sure if this is called brainstorming ;-). Anyway.. here for reassurance the psychedelic journey in and back again:

        ani4.gif

          V
          24-Ruby IV
          ValeryOchkov24-Ruby IVAuthor
          24-Ruby IV
          March 1, 2022

          Chaotic behavior in an algorithm to escape from poor local minima in lens design (optica.org)

          See color pictures in this article

           

            V
            24-Ruby IV
            ValeryOchkov24-Ruby IVAuthor
            24-Ruby IV
            September 13, 2022

            I propose a sketch of a tattoo - one of the faces of the goddess of mathematics Athena - the face of applied mathematics. An applied mathematician or programmer can come to a tattoo salon and order such a tattoo on his body.

            Portrait.png

            And speaking seriously, we can say the following.
            The theme of the portrait of the roots of a system of two equations is presented in the first chapter of this book.

            STEM Problems with Mathcad and Python - 1st Edition - Valery Ochkov - (routledge.com)

            Go to the site and order not a tattoo, but the book itself 😉

            V
            24-Ruby IV
            ValeryOchkov24-Ruby IVAuthor
            24-Ruby IV
            September 22, 2022

            The article on this problem

            Mathematics | Free Full-Text | Visualization in Mathematical Packages When Teaching with Information Technologies (mdpi.com)

            See the attach

             

            One part of the article. 

            WE.png

            Thanks, Werner, onr more! I have a dream to be your coautor.

             

            V
            24-Ruby IV
            ValeryOchkov24-Ruby IVAuthor
            24-Ruby IV
            February 11, 2024

            SMath: the built-in faction roots vs the user function Newton 

            2-17.png

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