title: find the periodicity of a modular function
body: <p>I created my own version of the fractal (which in fact takes the same principle as the Pythagorean tree).</p>
  
  <p>If you want to know what this gives you can do a little tour here.</p>
  
  <pre><code>    var myCanvas = document.getElementById('cnv');
      var ctx =  myCanvas.getContext('2d');
      myCanvas.style.backgroundColor =  "rgba(0, 0, 0, 0.1)";
  </code></pre>
  
  <p>My draw function like this. </p>
  
  <pre><code>  function draw(x, y, len, angle) {
      ctx.beginPath();
      ctx.save();
      ctx.translate(x, y);
      ctx.rotate((angle * Math.sin(len)) );
      ctx.moveTo(0, 0);
      ctx.lineTo(0, -len);
      ctx.stroke();  
      ctx.strokeStyle = "grey";
  
      if(len &lt; 1) {
        ctx.restore();
        return;
      }  
      var slider = document.getElementById("myRangeAngle");
      slider.oninput =  function() {
        var  p = document.getElementById('p');
        p.innerHTML = "L'angle : " + slider.value;
        ctx.clearRect(0, 0, 1366, 900);      
        draw(550,578,120,0);
      }
     draw(0, -len, len*0.7, - slider.value);
     draw(0, -len, len*0.7, slider.value);
     ctx.restore();
    }
  
    draw(550,578,200,0);
  </code></pre>
  
  <p><a href="https://codepen.io/m-metore/pen/Mxvqdq" rel="nofollow noreferrer">https://codepen.io/m-metore/pen/Mxvqdq</a></p>
  
  <p>Here is my problem I have an iterative function, U0 = 200; A + 1 = A * 0.7</p>
  
  <p>or Un = U0 * 0.7 ^ n.</p>
  
  <p>Then I multiply my angle x in (rad) by this formula:</p>
  
  <p>f (x) = x * sin (Un).</p>
  
  <p>My question is is there an integer x for which (fx) gives an integer.</p>
  
  <p>In other words, we must solve x * sin (U0 * 0.7 ^ n) = 2 * PI; (where x and n are integers) and we look for x (which is an integer)
  I specify that U0 = 200;</p>
  
  <p>I do not think there is an x such that this equation is true. Do you have any idea of how to prove it?</p>
  
  <p>thank you</p>