Pattern 1 - Geometric Zen
Inspiration: 
A geometric pattern with a zen or ancient coin-like vibe
Starting point - create a grid of interlocking circles. I made a square grid, then a second square grid moved over and up by the distance of 1/2 a square length. Then I wanted a circle at each corner. Explode gave me the corners. This resulted in a list of 5 points for each square, with the origin doubled. Maybe flatten that into a list and somehow remove the duplicates? I found Cull Duplicates (CullPt) to remove the duplicates and give me a list of points, nice! Let's just put a circle on each.
Then I made an octagon (in Rhino), set the curve in Grasshopper, and used a quick rectangle mapping to map the bounding box of the octagon into both grids.
Cool patterns!
Added a different radius for one of the sets of circles with a Number Slider, which gave even more variety - the parametric modeling quickly resulted in a variety of patterns I hadn't even considered.
So much fun! Several of the results are reminiscent of the inspiration pattern.
And I realized I didn't need to take make my own points for the first grid, I can just use the points output, so I cleaned that up a bit to simplify. Still need the second move to use the cells output for easy rectangle mapping of the hexagon, so I'll leave that as is.
Just playing around, I added a 4 point star as a curve, and previewed off one of the circles...
Now it's more like a Kaleidoscope!
These patterns are impractical for cutting, but could be printed - I would love them for wrapping paper or a notebook cover.
Pattern 2 - Seaweed
On to another pattern, using move vectors instead of a grid this time.
Inspiration: 
An organic curve inset in columns
This one started as a curve in Rhino, that I set in grasshopper. I then rotated the curve so it would be symmetrical.
Instead of having the pattern touch, I initially added space between the moves so there would be distinctive openings, which could perhaps be fabricated. The gaps between the shapes vertically and horizontally are all adjustable. The first result looked more like flames or waves than my inspiration, so I brought the curves back together to touch.
I had a bit of challenge with merge/ join and introducing a series to move this pattern, so that is disabled in the Grasshopper Definition.
For a twist, I added Rotation on the base curve to get a different Seaweed shape.
