I tried to make a rug using the Log Cabin pattern from Mason Dixon Knitting, and I got as far as one square, and I quit. I like to knit. I don’t like to stop knitting and cast off, and then pick up stitches or cast on again.
The square from Mason-Dixon is in the lower right. Strictly speaking, it does match a “log cabin” quilt square, with the rectangles and square corners. However, it’s a PITA to knit. The square in the upper right was knit as two triangles, increase at one edge to create a right triangle, and then coming back in the other direction and picking up one stitch per row at the diagonal edge to build a completed square. I only had to pick up one stitch per row, rather than the hundreds required of the other version.
Here’s a detailed picture of the triangular version:
and here’s a picture of a complete rug knitted with this version of a log cabin square:
I believe I get exactly the same effect as a “real” log cabin pattern with less than 1/100th of the parts of knitting I don’t like. (BTW, the gauge on this is 2 stitches to the inch.)
In time, I learned to knit squares diagonally and manage stripes of color on the diagonal to get a similar effect. Working in full-square units allowed me to manage the “extra stripe” you get on the wrong side of garter stitch. Looking at the same picture as is shown above, you can see these squares in the center of the bottom row.
One of these days, I’ll write up these patterns. I knit “by ear” and rarely use a pattern for the individual units, although I will sometimes use graph paper to manage color changes.