Paradox Fun

You may have noticed that I do enjoy doing zentangles from time to time. When I first heard about them, I would try to find patterns that I could figure out how to do on my own. As I have learned more I have sometimes found that my idea of how to do a pattern was different and often harder than the correct way. There is a wonderful website, Tangle Patterns, that has links to how-to's for all sorts of patterns.
One of the things I learned from a link on that site is how to draw the pattern Paradox. It is one of my favorite patterns now that I know how to do it. It is almost ridiculously easy, but until I saw the directions I could not figure it out. Oh, I tried, but I made it much harder than it needed to be. And it didn't look anywhere as nice. It might have been possible for someone to figure out that I was trying to draw Paradox, but that is as close as I ever got on my own.
Armed with the knowledge of how to do the pattern, I came across a zentangled drawing that the artist alleged was from Paradox, but that was beyond me. I saw it or similar designs more than once and stared at it until I figured it out. They look something like this, which was my first attempt at it.I was very pleased with myself for figuring it out and thought I would show you how to do it, too.
The first step is to learn how to draw the basic Paradox. The same method can be used to fill in shapes other than triangles.
Next, divide the area you will be filling into smaller areas for the individual Paradox patterns. On the top of the first one I did (above) it happened to form an sort of star pattern that I wanted to try to duplicate so I drew this:
Then I started filling in the shapes with the Paradox pattern. Here it is with just the upper right area filled in:
Each space was then filled with the Paradox pattern working each time in a clockwise direction. That is what gives those S-column (for lack of a better word) shapes where two Paradoxes meet. If you look carefully you can see that I have kept the pictures of these three steps oriented the same way to make it easier to believe it is that simple.
Next, I tried dividing a space into six (an even-number) shapes radiating from a sort-of center point. Sorry there is no before picture. I wanted to see what would happen if I alternated the direction of the Paradoxes as I filled in the shaped. For instance, in this example the upper right shape is done clockwise while the upper left shape was done in a counter-clockwise direction.
It is the change of direction that gives the fans and points of this design.

Last, I wanted to show you this envelope I recycled using the same idea. This was done while I was watching TV with my daughter. After I had filled in a couple of shapes she looked over and asked me what had happened to the first two shapes I had drawn. The pattern overwhelms the initial shape it fills.
It is something you almost have to try to understand. Or at least that is how my brain works.