I just uploaded my

**project to my Scratch page. Here’s a screenshot of the fourth iteration of the curve and the link to the project.***Scratch Hilbert- space-filing curve*
http://scratch.mit.edu/projects/popswilson/3278475

The curve is a one-dimensional line that fills a
space! If you want to know the mathematics underlying that astonishing fact I
recommend you click on this link and download and read the article,

*Crinkly Curves*, by Brain Hayes. I never miss reading his column as I subscribe to the*American Scientist*.
http://www.americanscientist.org/issues/pub/crinkly-curves

His blog also contains a post with even more information about the Hilbert curve.

http://bit-player.org/2013/mapping-the-hilbert-curve

Dr. Hayes has also posted a wonderful Hilbert curve 'extra' that has an interactive section that maps the points on the unit line interval to the points of the unit square.

http://bit-player.org/extras/hilbert/

I first
learned about “pathological curves” like the Hilbert curve when I read the
following column. It’s an old article but mathematics is

*timeless.*Try to find Martin Gardner’s*Mathematical Games*column that appeared in the December 1976 issue of*Scientific American*magazine. The column is titled*In which “monster’ curves force the redefinition of the word “curve”.*
Here’s is an
update to that column.

When home computers first appeared—soon after the column was
published—I enjoyed programming such curves in Logo.

I have also written a PDF file,

*The Hilbert Curve in Scratch,*that describes the programming side. A simple email request is all I need.