What is a Golygon?

Golygons were defined by Dr. A. K. Dewdney in his Mathematical Recreations column in the July 1990 issue of Scientific American. Here is what he wrote:

<< Correction: The word "golygon" is Lee Sallows invention and not Kee Dewdney's as I stated. Lee corrected me via email on January 20, 2001 >>

"Allow me to start you on a journey in Golygon City. You can take a similar trip in New York, Kyoto or almost any large city whose streets form a grid of squares. Here are your directions. Stroll down a city block, and at the end turn left or right. Walk two more blocks, turn left or right, then walk another three blocks, turn once more and so on. Each time you turn, you must walk straight one block farther than before. If after a number of turns you arrive at your starting point, you have traced a golygon. If you do not need the physical exercise, you can easily simulate the journey by moving a pencil along a piece of graph paper with a square grid. If you become lost, you may refer to the map below."

"A golygon consists of straight-line segments that have lengths (measured in miles, meters or whatever unit you prefer) of one, two, three and so on, up to some finite number. Every segment connects at a right angle to the segment that is one unit larger-except the longest segment, which meets the shortest segment at a right angle. Golygons are more than just a geometric curiosity. They have inspired some delightful puzzles as well as some intriguing problems for research. What better way to develop insight into the research process than to take a recreational journey?"

The reason he called them Golygons is that their mathematical name is "Serial Isogons of 90 Degrees."