This is a wonderful gift for the science geek in your life.
I recently stumbled onto this website devoted to knitting interesting pieces such as visual illusions and math-related designs. I was impressed with much of the work, but even more intrigued by the ideas. I taught cognitive psychology for a decade and, at least in the classroom, perception was a specialty (I will be posting more perception-related instructables soon). I am not much of a knitter, but I have been an avid crocheter since my neighbor taught me to chain at age 7.
Coincidentally, I was also looking for projects for holiday gifts for my sons' teachers at the time and this gave me a few ideas. One idea sparked another, and the next thing I knew I had designed several pieces. This is one that I completed and gave to my 8th grader's science teacher.
This illusion (dubbed "Munker-White" for two people who discovered versions of it) is a result of the way our visual system determines the brightness and color of an object (or part of an object), which includes comparing it to surrounding colors. The illusion itself works with various colors, but is easiest to reproduce with black, white, and a medium grey. When the mid-brightness color is viewed with the darkest color, we perceive it as darker than when it appears with the brightest color. For example, the grey bar in the box (second image) is a single shade. Try covering the background and you'll see it differently. Likewise, the pink bar of stripes in the middle of the third image is a single shade of pink. When a mid-brightness color is chromatically different from the stripes, its hue appears to shift. For more demonstrations/versions of the illusion, I recommend this website.
The illusion is not as strong when viewing the scarf in 3D and in person, but it is apparent.
I apologize for the lack of images for intermediate steps. The pattern I provide assumes knowledge of crochet techniques and stitches, but it is not a difficult pattern for a beginner. If you are new to crochet, I recommend using Google to find one of the many instructional sites or purchasing any pattern book. Everything you'd need to make this scarf would be covered in most books. Most importantly, learn to change colors without carrying the yarn.
The scarf pictured here is the one given to the teacher. I made some small changes to the pattern when I began a second scarf (still in progress), so you might notice that the image does not match the pattern exactly.
Step 1: Materials
You will use approximately half of each skein of the two main colors; remnants will do for medium color. A medium weight (worsted is good) works best.
For the scarf shown I used:
1 skein each of Hoops & Threads Impeccable™ in black, white, and true grey
Size H crochet hook
Step 2: Crochet!
This piece is worked horizontally. The finished scarf is approximately 70" long and 5" wide. Adjust the length by adding to or subtracting from the first chain. Increase the width by adding rows, two at a time. I do not recommend subtracting rows.
ch = chain
dc = double crochet
st(s) = stitch(es)
Color A = dark (black in example)
Color B = light (white in example)
Color C = med (grey in example)
With Color A: ch 232
Row 1: dc in 4th ch from hook, dc 8, change color to C: dc 15, change to color A: dc to end, change to color B: ch 3, turn.
Row 2: dc in 4th ch from hook, dc 8, change color to C: dc 15, change to color B: dc to end, change to color A: ch 3, turn.
Rows 3-8: repeat rows 1 & 2, fasten off.
Step 3: Clean Up
Weave in loose ends.