Argyle Cascade is the first AutoScarf pattern. It's a great starting point because the motif is easy to see as you work it up, and the rule is simple to follow as you stitch. The geometric motif grows row by row from just two things: your first two rows of stitches, and one easy-to-remember color rule. The color rule is based on a mathematical algorithm called a cellular automaton, but implementing it for each stitch is as simple as noticing the colors of three nearby stitches. The "pixie stitch" used in this pattern consists of rows of two-color stitch clusters with carried yarn caught in specific ways to interlock stitches and create clean pixellated motifs.

MATERIALS

Yarn: Worsted-weight yarn in two contrasting colors. Yardage depends on desired length of scarf.

Tools: Crochet hook in size appropriate to your yarn and tension, plus scissors and a darning needle for finishing.

Example: The sample in the photo above was crocheted with Malabrigo Rios worsted-weight yarn and a US G (4mm) hook.

GAUGE

Measurements: This pattern is for a scarf, so there are no required measurements. The project should be fun to crochet for YOU, so adjust to what you think feels and looks the best.

Swatching: We suggest creating a swatch of 8-10 rows in the same width of the desired scarf, and experimenting with tensions and hook sizes. Try to form stitches that are kind of "bouncy" and keep the work snug without pulling on the yarn. Find that middle ground where the color transitions are the most hidden.

Example: The sample in the photo above has 13 stitch clusters in each worked row. The rows are interlocked in pairs, so there are a total of 26 stitch clusters across the work. Our gauge and tension resulted in a scarf that measures 5 3/4 inches (14.5 cm) across. This sample has 18 interlocked stitch clusters (9 in each worked row) for every 4 horizontal inches, and 10 stitch clusters for every 4 vertical inches.

ABBREVIATIONS

• MC = main color of yarn
• CC = contrast color of yarn
• ch = chain stitch
• sc = single crochet stitch
• hdc = half-double crochet stitch (US version): yarn over and pull up a loop, then yarn over and pull through all three loops
• 2hdc = a cluster of two half-double crochet stitches worked into the same gap

COLOR RULE

Each AutoScarf "designs itself", in the sense that the color used for each stitch is completely determined by the colors of nearby neighbor stitches in the rows below. We have provided a color chart for this pattern which you can follow if you like, but the magic of this pattern is that you do not need a chart!

The image below illustrates the interlocked structure of the pixie stitch pattern. The trapezoids represent the 2hdc clusters you will work across each row. You will work on each side of the work from right to left, and each row of clusters will be worked into the gaps between clusters in the row below. (If you're left handed and crochet the other way, just reverse the direction.) Before you form a new stitch cluster S, you will decide what color to use by applying a simple rule based on the colors of the neighbor stitch clusters L, R, and C to the left, right, and center.

The color motif in this pattern will use "Rule 150". This is the name of the rule because it happens to be determined by binary signals 1, 2, 4, and 7, and because $2^1 + 2^2 + 2^4 + 2^7 = 150$. But you don't need to worry about any of that! The rule has a very easy-to-remember interpretation:

Every cluster of stitches in the pattern after the first two rows will follow this color rule. The result is the 2-color color chart shown below.

COLOR CHART

The color chart illustrates both a long stretch of the pattern and a close-up of the initial rows of the scarf. The motif repeats after row 27, as indicated by the bracket. After the chain and setup rows, start with Row 1 at the bottom of the color chart. Odd rows are worked and read right-to-left. Even rows are stitched on the other side of the work; read the chart from left-to-right as you physically stitch right-to-left. Each trapezoid in the color chart represents a 2hdc cluster.

The initial two rows at the bottom of the color chart follow a specific color pattern. After those two rows, the rest of the color chart is determined by Rule 150. The entire color chart above can be summarized in just four lines of text:

If you change the color pattern in Row 1 and/or Row 2 and then follow Rule 150 after that, then you can produce a different color pattern in a similar style. You can experiment with different initial rows by mapping it out on paper or by using the AutoScarf Motif Maker at autoscarf.org/motif-maker.

STITCH CHART

The stitch chart below shows the arrangement of stitches in the pattern. The long "T" symbols are each one hdc, and the "oval" symbols are each one chain stitch.

PATTERN INSTRUCTIONS

Before you start: Read the Special Techniques section below. These techniques are what make the pixie stitch work beautifully and are essential for quality results.

These row-by-row pattern instructions describe what stitches you'll work in each row. To determine colors, refer to the color rule or color chart above—they work in conjunction with these instructions to guide you through the pattern.

In these instructions we will assume that you are following the color chart above. If you change the color pattern in the initial two rows then you will have to update the pattern accordingly. This pattern is for rows of $n=13$ clusters. It can be adapted to rows with other odd numbers of clusters if desired by starting with $2n+1$ chains and choosing initial color patterns of length $n$ in Row 1 and Row 2.

Foundation Chain: Chain 27 at an even, bouncy tension in MC.

Setup Row: Chain 2 more. Start carrying CC now by laying tail across the working yarn. Hdc in each back bump, starting with the fourth bump from the hook, across the entire row, in MC. Work over the carried yarn through the entire row, adjusting tension of the carried yarn at the end as needed. In the last stitch don't work over the carried yarn, keep it to the back. You should have 27 hdc stitches. Turn.

Row 1 (Initial Color Pattern): Chain 2 in the color of the first cluster, switching colors in the first chain if needed. Stitch clusters of 2hdc in every other gap between stitches (not into the tops of the stitches), starting after two hdc stitches of the previous row as shown in the Stitch Chart. Always work over the carried yarn and also catch the carried yarn from the previous row in each cluster (see Handling Carried Yarn). Use CC in clusters 1, 6, 7, 8, and 13, and MC in all others (see Changing Colors). Work the last 2hdc cluster as specified in Special Techniques (see Working the Last Cluster). You should have 13 clusters. Turn.

Row 2 (Initial Color Pattern): Chain 2 in the color of the first cluster, switching colors in the first chain if needed (see Starting a New Row). Stitch clusters of 2hdc in each gap between clusters across the entire row, all in MC. In each cluster, work over carried yarn and also catch the carried yarn from the previous row. Work the last cluster as specified in Special Techniques. You should have 13 clusters. Turn.

Row 3+ (Rule 150 Begins): From Row 3 onward, apply Rule 150 and/or color chart to determine stitch colors for each cluster (stitch in CC when either 1 or 3 neighbors are in CC). In each row, continue to work over carried yarn and also catch the carried yarn from the previous row. Start with chain 2 in the color of the first cluster, switching colors in the first chain if needed. Stitch clusters of 2hdc in each gap, working the last cluster as specified in Special Techniques. You should have 13 clusters. Turn and repeat until your scarf is the desired length.

Borders: When you are done with the scarf you can add borders along each side, if you like, by working 2hdc clusters into each of the 2ch gaps along each side of the work.

SPECIAL TECHNIQUES

Overall, the pixie stitch crochet pattern is simple; it's mostly half-double-crochet. Adding the following special local techniques will enable you to manage carried yarn effectively and hide color transitions on both sides of the work. These are the tiny details that are often left out of pattern instructions; we include them so that you can create the best work possible. Using these techniques will significantly increase the quality and reversibility of your scarf.

Handling Carried Yarn

These instructions are the magic sauce that makes the pixie stitch "interlocked".

• Always carry non-working yarn: The non-working yarn should be carried across all rows, even if it is never used in the row. If you skip this step then your stitches will not interlock. Hold the carried yarn together with the top of the work and stitch over it as you go. It helps to hold the carried yarn close against the work and slightly to the front of the side facing you.

• Always catch previously carried yarn: When inserting yarn into the row below, go below the strand that was carried along that previous row and catch it in your stitch. Be sure to catch only the previously carried yarn, and not part of the stitch in the row below.

Changing Colors

These instructions are the magic sauce that hides pixie stitch color transitions and makes the work look good on both sides.

• Change colors at the end of the previous cluster: Before finishing the last stitch of a cluster, decide if a color change will be needed for the next cluster. If a change is needed then follow the instructions below to finish the stitch.

• Adjust carried tension before changing colors: Before finishing that last stitch, pull on the carried yarn to fix its tension under the earlier worked stitches. Then pull the work itself horizontally to make sure you didn't pull the carried yarn too tightly; you want some bounce in it so you can catch those loops in the next row. Make sure to adjust tension all the way back to the last time you stitched with the carried yarn.

• Pull old yarn in front: Before the last yarn over of the last stitch in the working color, bring the working yarn to the front of the work. Pick up the carried yarn and start working with it by finishing the hdc (yarn over and pull through three loops on hook). Bringing the yarn in front before each color change will twist your yarns, and over time you'll have to stop and untwist them. However, it is necessary because it completes the fourth back leg of the last completed hdc, and hides the color transition fully inside the hdc stitch.

• Tug on the leg: The last front leg of the stitch you just finished may be a bit loose, which can cause tension issues later. Tighten this last leg by tugging on the new carried yarn (previous working yarn) before continuing the next cluster in the new color.

Working the Last Cluster

Edge clusters are worked slightly differently in order to keep carried yarn away from the edges of the work. This results in much cleaner edges.

• Color of the last cluster: Before finishing the second-to-last cluster, compute the color for the last cluster. The last cluster has no left neighbor in the previous row; "wrap around" and use the stitch on the other side of the row. Finish the second-to-last cluster with the color needed for the last cluster.

• Working the last cluster: The last cluster is a 2hdc as usual, but worked in a different way than the other clusters. Start the first hdc in the 2ch gap at the edge of the work (yarn over and pull up a loop), working over the carried yarn as usual. Before finishing that first hdc, pull the carried yarn to the right in back of the work so that you are not working over it anymore. Finish the hdc and do the second hdc to finish the last cluster of the row.

Starting a New Row

Each row starts with a 2ch and possibly a color change, depending on the chart/rule.

• Chains before the first cluster: After turning the work make sure both yarns are in front. Before starting the row, calculate the color of the first cluster. If no color change is needed then 2ch in the working color to start the row. If a color change is needed then make the change with a chain stitch, then chain one more stitch in the new color; keep the old color in front so that it pulls across the work and hides the color transition in the next step.

• The first cluster: Pull the carried yarn to the left and work the first 2hdc cluster over it, while catching the previously carried yarn below as usual. You may have to pull on the yarn to adjust tension and hide any color transition.

Variants

Each of the motifs below uses Rule 150 throughout and has the same style and spirit of Argyle Cascade. The only difference from the core motif is that we have chosen slightly different locations for CC in the first row; in these examples the second row is still all MC.

You can change the Argyle Cascade motif in many different ways depending on where the CC is stitched in the first two rows. You can also change the motif anywhere in the middle of the scarf if you want to change things up; all you have to do is change one or more of the color assignments in a row (or make a mistake and keep it), and then continue in Rule 150. You can create other variants yourself by using the AutoScarf Motif Maker at autoscarf.org/motif-maker.

DESIGNER NOTES

How to get started if you're a beginner

The most difficult part of this (any?) crochet pattern is getting started with the foundation and first few rows. If you have a friend who knows how to crochet, ask them to start the scarf for you. It will be much easier for you to learn and work from a solid starting point. By the time you finish your first scarf or swatch, you will be better at setting up the initial rows for your next attempt.

If you make a mistake

This is a scarf. Be kind to yourself and go with the flow. The scarf will still look great even if you miss a stitch, misapply a color rule, or deviate from the chart. Here are some of your options:

• Leave it: Just keep going. Keep following the color rule and see what happens. The motif chart won't apply to you anymore but remember that you don't need it! The scarf doesn't have to match the chart, and the color rule will tell you what to do in each row. You will make your own unique thing.

• Correct your mistake: With crochet, it's easy to rip back crochet stitches and redo whatever error occurred. If your mistake breaks the motif symmetry or changes the width of the scarf, it may be worth ripping back.

• Start over: If you haven't done very many rows and something is going sideways, then you could consider just starting over. Making the scarf longer won't fix errors or tension issues in your starting rows. It's completely normal to start over a few times as you get the hang of the pattern and special techniques; you're learning and swatching as you go.

Counting stitches

This pattern is part of the AutoScarf project, in which people from all over the world are working together to hand-craft one million algorithmic stitches. We stitch math! Please consider adding your project and your stitches to the count at autoscarf.org. Each 2hdc cluster counts as two stitches. Help us get to one million!

Why we started AutoScarf with this pattern

Many, many color patterns can be made from different initial row patterns, different color rules, and even different types of stitch structures. Why this one? We chose Argyle Cascade for the first AutoScarf pattern for three reasons. First, the interlocking pixie stitch structure uses techniques that are very similar to those that we used in the recent Granny Life community art project (grannylifecrochet.com), so we knew a lot of people would already know how to do most of the "Special Techniques" listed above. Second, Rule 150 and the particular initial conditions chosen for Argyle Cascade combine to make a very straightforward color pattern. The left/right symmetry and large areas of each color make it easy to follow the color rule and check as you go if your pattern is correct. Finally, we love the playful nature of this motif; in particular, the way that the cascading structures combine in positive and negative space to make argyle diamonds. Such complexity in such a simple form!