[![enter image description here][1]][1][![enter image description here][2]][2][![enter image description here][3]][3]I am a newbie to Blender who is realizing i need to slow down and learn the basics.  I can use a curve and array modifier to make an object fill up and follow this curve.  I'm assuming there is a way to get this cylinder to appear to be endlessly generating from the origin. Is the only way to do this to set up a procedural animation?  I'm pretty confused and especially confused by the procedural stuff.  thanks.  
[![enter image description here][4]][4]


  [1]: https://i.sstatic.net/RZI8j.gif
  [2]: https://i.sstatic.net/yPzJm.jpg
  [3]: https://i.sstatic.net/XfjNd.gif
  [4]: https://i.sstatic.net/3i7Wi.gif