Crochet the following 2 models:
1. Crochet a plane – 12 x 12. Twelve rows with twelve stitches per row.
Detailed diagrams and instructions are in this PDF document:
CROCHETING A 12 X 12 PLANE
Foundation Row: Crochet 12 chain stitches plus 1 turning chain.
Row 1: Turn your work so the last chain you made (the turning chain) is now on your right. Skip the turning chain and make one single crochet (sc) stitch in each chain of the 12 chains. Finish the row by making one turning chain.
Row 2: Turn your work so the last stitch you made (the turning chain) is now on your right. Skip the turning chain and make one sc in each of the 12 sc stitches from row 1. Finish the row with a turning chain.
Rows 3 through 12: Repeat Row 2.
2. Crochet a hyperbolic plane. Start with a foundation row of 12 chains and then make 12 rows using single-crochet stitches. Increase in every 4th stitch (N=4) in each row.
Detailed instructions and diagrams are in this PDF document:
Instructions for Crocheting a Hyperbolic Plane
For more inspiration see these pictures:
What if you increased in every other stitch?
What if you increased in every stitch?
What if you increased at a different rate in each row?
What if you started out with a longer foundation row?
What if you increased at random rates?
What if you started with a circle of chains for a foundation row instead of a line?
Another version of instructions for crocheting a hyperbolic plane