25 Mar 2002 I thought I'd put something a little more concrete in here. I do tend to spout off, philosophize, etc. To paraphrase, opinions are like parents -- everybody has them (and nobody particularly wants to meet them, which extends the original simile (if you don't know the original simile, I'm not going to tell it to you -- just think of things everybody has)). (Speaking of opinions, and random spouting, let me impart my latest thought - on the phrase "blind as a bat" (also a simile, lookee that). Now many bats are blind, but some have some limited sight, and to a large part the bats don't need the sight to survive, thank you very much. Such a phrase indicates our own biases towards sight in human civilization, and even though we may concede that blind bats seem to manage to eat and mate without visual cues, we may say "ah, but those bats are missing the beauty of a moonlit night." Hey, those bats might think us lacking the experience of the 3-d world, and world of trajectories and surfaces... just as dogs might feel sorry for their smelling-impaired masters. Anyway, I just think "blind as a bat" is a weak simile; why not "blind as a busy man"? It's even sadder when one has a sense but doesn't ever experience the beauty of the world through that sense.) In any case, for some time I've been quite the crafter -- I knit, crochet, cross-stitch. For the most part, I use patterns made by other people, though I invariably change them, due to my own mistakes, the materials I'm using (or lack thereof), or personal purposes. For example, I just took a simple teddy bear pattern and did the bear in green. Then I added spikes to the back and a long lizard tail -- Bearzilla! I like making personalized presents (Bearzilla is for my ma). However, a couple times I've designed my own patterns. Once I came up with an angel pattern, I've made a braided cross pattern, and I did a personalized wedding gift for a high school friend, by making a pattern where his and his wife's names were done as mirror images of each other. I usually just sit down with some graph paper and draw out the patterns. But sometimes I use math. Once I did a cross-stitch pattern for a friend, where I came up with a cellular automaton pattern based on a nickname and using his initials from other names as seeds. A cellular automaton is a mathematical construct where there are cells in a regular pattern - usually a square grid - and a discrete set of properties for each cell, such as color, or whether a cell is "on" or "off". The most famous example is John Conway's "Game of Life", which is a 2-dimensional cellular automaton that "evolves" over time, and the cells are either "occupied" or not, which is usually represented as colored in or not (sometimes the colors are based on how long the cell has been "alive"). Well, a pattern that changes over time isn't exactly the easiest to replicate on graph paper for a cross-stitch pattern, so instead of a fluctuating set of rules, I made an automaton that only grew -- cells never died. I called it the "kudzu automaton" in honor of my friend's nick "kudzu". Years passed, and then I came across an article in Knitter's Magazine. It mentioned using cellular automata for knitting lace patterns, cabled patterns, fair-isle patterns, etc. It used a cellular automaton that is 1-dimensional (after all, knitting and crochet build up row by row, not a 2-d field like cross-stitch) that I recognized to be the generator for the Sierpinski gasket. So I tried this with knitting, but knitting is too easy to screw up and too hard to fixed once one has screwed up (and besides, I'm not good at lace knitting.) So I adapted the technique for crochet to make a large fractal shawl. In crochet, one has only one active stitch at a time - you can't drop the entire row - and it's easy to see what the neighboring cells are in the previous row in crochet. I am willing to teach anybody to crochet, but it's much easier to do it in person. For those interested in mathematical crochet, I can teach people to crochet the hyperbolic plane, which is even easier to do, as one needs only to know how to chain and do the single crochet stitch. I found the pattern online, and if you wish to learn to crochet, I recommend going to the web site of the Craft Yarn Council of America (headquartered in Gastonia, NC, I believe). So here's the pattern: ch = chain ch-sp = chain space dc = double crochet (the american definition) This pattern is adaptable to any yarn, any size hook. Once you get started, you just need to remember the cellular automaton rule. So here it is: Row 1: Ch 4. 2 dc in 1st ch - 1st row, counts as 3 dc. (the turning chain is 3 ch, and counts as one dc). Ch 3, turn. Row 2: 1 dc in 1st dc, Ch 1 & skip middle dc, 2 dc in last dc. (so looks like - 2 dc, ch-sp, 2 dc) Ch 3, turn. Row 3: 1 dc in 1st dc, Ch1 & skip next dc, dc in ch-sp, ch 1 & skip next dc, 2 dc in last dc. (looks like: 2 dc, ch sp, dc, ch sp, 2dc) Ch 3, turn Ok, the first couple rows go by this rule, but here it is: You're going to add a dc at each end for each row (that's the 1 dc in the 1st, + the turning chain at the beginning, and the 2 dc in the last dc); this gives the standard triangular shawl shape. One starts at the tip and works until the triangle is as large as you wish. Now, you're going to be looking at the previous row while you build up your current row. The rule is to look at the two "areas" neighboring your current area in the previous row. If there's two spaces, or no spaces, you simply do dc's straight. If there's exactly one space , make a ch1-sp, then dc. So let me show how this works on the 4th Row: So you've done the turning chain and 1 dc in the 1st dc. (You've just added a new "area") Looking at the previous row, you see a ch-1 sp immediately to the left and two dcs to the right. So looking at my rule - exactly one space, make a space - I ch 1, skip a dc, and dc in the ch-sp in the row below. Second area done. Now, I look below, and I see a ch-sp to the left, and a ch-sp in the right. My rule: two spaces beget no spaces, so I do 1 dc each in the next two dcs. Third area done. Finally, I see the ch-sp to the right, and 2dcs to the left, so exactly 1 sp. So I ch-1, skip the dc and dc in the next (and last dc). Fourth area done. Finally, one more dc in the final dc, to add an area on the end. So the pattern of the 4th row looks like: 2 dc, ch-sp, 3dc, ch-sp, 2dc. Just to let you know, the 5th row looks like: 2 dc, ch-sp, 1dc, ch-sp, 1dc, ch-sp, 1 dc, ch-sp, 2 dc. 6th row: 2dc, ch-sp, 7dc, ch-sp, 2dc Those are just to let you check to see if you understand the rules. If you do this correctly, on every row there should be 1 ch-sp at the very beginning and 1 ch-sp at the very end. Some of the rows will have nothing but dcs and no spaces. Some rows will be completely full of ch-1, 1dc blocks. There's actually a mathematical pattern as to which rows this occurs upon, and if you =really= care, you can figure it out. (Hint: It's related to powers of 2)

Prev | Year | Next |