Linear Systems Hat in Spud & Chloe Fine - Downloadable PDF

Linear Systems Hat in Spud & Chloe Fine – Free Knitting Pattern by Ann Weaver

The Linear Systems Hat is a free downloadable knitting pattern designed by Ann Weaver and published by Spud & Chloë. This intermediate-level knitted hat features stranded colorwork worked in the round, combining a classic ribbed cuff with a patterned body to create a structured, visually striking finished piece. The pattern is available in three sizes, making it a versatile project for knitters looking to practice or expand their two-color knitting skills.

What Is Being Made

This pattern produces a knitted hat worked entirely in the round from the cast-on edge at the brim up through the crown decreases. The design incorporates a two-color stranded colorwork motif across the body of the hat, giving it a bold linear aesthetic that is referenced directly in the pattern's name. Three sizes are offered — small, medium, and large — achieved by varying the number of cast-on stitches: 108, 126, or 144 stitches respectively.

Techniques Used

• Stranded colorwork – The body of the hat is worked in stranded stockinette stitch, where two colors are carried across each round. This technique requires knitters to manage tension carefully so that the "floats" — the strands of yarn carried behind the work — do not pucker or pull the fabric.
• Working in the round – The entire hat is knitted circularly, first on a 16-inch circular needle and then transitioning to double pointed needles (dpns) as the crown decreases reduce the stitch count and the circular needle becomes too large.
• Ribbing – The cuff is worked in a 1x1 rib (knit 1, purl 1) for approximately 2½ inches, providing a stretchy, fitted edge that keeps the hat securely on the head.
• Crown shaping and decreases – The hat is shaped at the top using standard knitting decrease techniques to taper the crown neatly.
• Joining in the round – Stitches are cast on and joined carefully to avoid twisting, a foundational technique for any circular knitting project.

Stitches Used

• Stockinette stitch (st st) – The primary stitch used throughout the hat body, creating a smooth, flat fabric ideal for showcasing colorwork motifs.
• 1x1 Ribbing – Alternating knit and purl stitches worked across the cuff section for elasticity and structure.
• k2tog (knit two together) – A right-leaning decrease used during crown shaping to reduce stitch count evenly.
• kfb (knit into the front and back) – An increase stitch referenced in the pattern's special abbreviations, used where shaping requires adding a stitch.
• Slip stitch (sl) – Referenced in the abbreviations for use within the pattern construction.

Materials

• Yarn: Spud & Chloë Fine — a 4-ply (fingering weight) yarn, sold in 65g/248-yard hanks. The pattern calls for 1 (2, 2) hanks in the main color (MC) and 1 hank in the contrast color (CC), depending on the size being knitted. Spud & Chloë Fine is known for its soft, kid-friendly fiber content and vibrant colorways, making it well suited to colorwork projects like this one.
• Needles: Size 3 (3.25mm) 16-inch circular needle for the body of the hat, and Size 3 (3.25mm) double pointed needles for the crown — or the size needed to achieve the specified gauge.
• Notions: Stitch markers to indicate the beginning of the round.

Gauge

Gauge is measured in stranded stockinette stitch at 28 stitches and 36 rounds per 4 inches