I thought I was somewhat good at maths but this problem has defeated me. I am now thinking that what I am trying to do is not possible.
I am trying to modify a crochet pattern of a 3d object in orded to make a mirrored version of that object. It is a curled "horn".
The full pattern can be found here: full pattern
The way the pattern works:
- It is a clockwise spiral, starts from the tip and ends at the bottom of the horn
- The rows are of 2 kinds (although it is a spiral so not actual "rows" but rows of the spiral if that makes sense)
Row type 1:
- Is the same length as the previous row. (Same number of stitches)
- Has varying thickness along its length: first part is taller, second part is shorter. The exact ratio of length of first to second part varies, but first part is always longer.
Row type 2:
- Is longer that the previous row. (More stitches)
- The additions of extra stitches are done in 3 places along the row, equidistant to each other.
- Is the same heigth along the entire row.
The object this generates is a curled horn, and the curling is clockwise. I want to make a mirrored object (curling counterclockwise). However the restriction is that the underlying spiral (the way that the rows are arranged) is still a clockwise spiral (in order to make a counterclockwise spiral I would have to work with my left hand or inside out, and neither is really realistic for this pattern).
I am not sure if this is geometrically possible. And I don't know how to work it out.
The pattern for the horn in crochet notation is pasted below. For those unfamiliar with crochet notation:
- sc: the most standard stich, a single square "pixel"
- hdc: a vertical rectangular "pixel" - taller than sc, but same width
- sl: a horizontal rectangular "pixel" - shorter than sc, but same width
- rounds with "2 sc in the nxt st" are the increase rounds, where 2 "pixels" are added atop one "pixel" from previous round, increasing the row length by 1
Rnd 1: 6 sc into the ring. – 6 sts
Rnd 2: 1 hdc in ea of the next 3 sc, 1 sc in ea of the next 3 sc. – 6 sts
Rnd 3: Rpt Rnd 2.
Rnd 4: Rpt Rnd 2.
Rnd 5: (1 sc in the next st, 2 sc in the next st) 3 times. – 9 sts
Rnd 6: 1 hdc in ea of the next 5 sts, 1 sc in ea of the next 4 sts. – 9 sts
Rnd 7: 1 hdc in ea of the next 5 sts, 1 sl st in ea of the next 4 sts. – 9 sts
Rnd 8: Rpt Rnd 7
Rnd 9: (1 sc in ea of the next 2 sts, 2 sc in the next st) 3 times. – 12 sts
Rnd 10: 1 hdc in ea of the next 6 sts, 1 sl st in ea of the nxt 6 sts. – 12 sts
Rnd 11: Rpt Rnd 10
Rnd 12: 1 sc in ea st around. – 12 sts
Rnd 13: (1 sc in ea of the next 3 sts, 2 sc in the next st) 3 times. – 15 sts
Rnd 14: 1 hdc in ea of the next 9 sts, 1 sl st in ea of the next 6 sts. – 15 sts
Rnd 15: Rpt Rnd 14
Rnd 16: 1 sc in ea st around. – 15 sts
Rnd 17: (1 sc in ea of the next 4 sts, 2 sc in the next st) 3 times. – 18 sts
Rnd 18: 1 hdc in ea of the nxt 12 sts, 1 sl st in ea of the nxt 6 sts. – 18 sts
Rnd 19: Rpt Rnd 18
Rnd 20: (1 sc in ea of the next 5 sts, 2 sc in the next st) 3 times. – 21 sts
Rnd 21: 1 hdc in ea of the next 13 sts, 1 sl st in ea of the next 8 sts. – 21 sts
Rnd 22: Rpt Rnd 21
Rnd 23: (1 sc in ea of the nxt 6 sts, 2 sc in the nxt st) 3 times. – 24 sts
Rnd 24: 1 hdc in ea of the nxt 16 sts, 1 sl st in ea of the nxt 8 sts. – 24 sts
Rnd 25: Rpt Rnd 24
Rnd 26: (1 sc in ea of the next 7 sts, 2 sc in the next st) 3 times. – 27 sts
Rnd 27: 1 hdc in ea of the nxt 18 sts, 1 sl st in ea of the nxt 9 sts. – 27 sts
Rnd 28: (1 sc in ea of the nxt 8 sts, 2 sc in the nxt st) 3 times. – 30 sts
Rnd 29: 1 hdc in ea of the nxt 20 sts, 1 sl st in ea of the nxt 10 sts. – 30 sts
Rnd 30: (1 sc in ea of the nxt 9 sts, 2 sc in the nxt st) 3 times. – 33 sts
Rnd 31: 1 hdc in ea of the nxt 22 sts, 1 stl st in ea of the nxt 11 sts. – 33 sts
Rnd 32: (1 sc in ea of the nxt 10 sts, 2 sc in the nxt st) 3 times. – 36 sts
Rnd 33: 1 hdc in ea of the nxt 24 sts, 1 sl st in ea of the nxt 12 sts. – 36 sts
Rnd 34: (1 sc in ea of the nxt 11 sts, 2 sc in the nxt st) 3 times. – 39 sts
Rnd 35: 1 hdc in ea of the nxt 26 sts, 1 sl st in ea of the nxt 13 sts. – 39 sts
Rnd 36: (1 sc in ea of the nxt 12 sts, 2 sc in the nxt st) 3 times. – 42 sts
Rnd 37: 1 hdc in ea of the nxt 28 sts, 1 sc in ea of the nxt 14 sts. – 42 sts
Rnd 38: Working in both of the top loops, 1 Sl st in each st around. Cut yarn and tie off, leaving a long tail for sewing.