A Penrose Floor

I have long been intrigued by geometric patterns.  As a teenager I made models of various polygons and polyhedra and learned the rules for constructing geodesic domes.  A book that held my fascination for years was “Shapes, Space, and Symmetry” by Alan Holden

The ability for computers to represent 3D objects and to realistically render them, to interact with them, and to display them in 3D was years in the future; in the 1970s, physical models were essential for teaching geometric principles and understanding crystal structures.  The author, a physicist and chemist, had crafted a lifetime of such models and described them in his book.  I could not match the patience and skill required to make his beautiful and complex cardboard models. 

Also in the 1970s, Roger Penrose, the British mathematician and scientific colleague of Stephen Hawking, investigated an arcane branch of geometry to answer the question of whether an infinite plane can be tiled with a set of shapes that did not overlap, have gaps, or repeat.  He found that the answer was yes, it was possible, and he discovered several sets of shapes that could do it.  The first set included pentagons, stars, “boats” and diamonds.  The second set was simpler, it needed only two shapes called kites and darts.  The third was simpler yet, a pair of rhombuses, skinny and fat parallelograms with equal length sides.  These sets of shapes, P1, P2, and P3 are known as “Penrose tiles”.

I’m not going to explain the mathematical concepts behind them, even if I could, but I will call attention to their esthetic beauty, which you can find by a simple Google search.  Penrose tiles became popularized by Martin Gardner’s famous Mathematical Games column in Scientific American in 1977, and suddenly everybody was making Penrose patterns out of them.  Penrose was able to patent the shapes, which were subsequently licensed for games and puzzles.  He famously won a lawsuit against a company that used their non-repeating feature to prevent their embossed toilet paper from sticking on the roll!

When presented with the “canvas” of the floor in my newly renovated screen porch, I immediately wondered how best to cover it.  I really liked the idea of ceramic tiles, impervious to rain and snow, and then realized this floor could be a host to the mathematical beauty of Penrose tiles! 

I researched the idea.  There were Penrose tilings in public spaces, famously at Texas A&M and more locally, Carleton College. I also encountered individuals who had made such patterns in their private homes.  I learned that this was not a project for the wing-it, make-it-fit crowd; the tile shapes needed to be cut to thousandth-inch precision.  I considered what was needed to cut ceramic tiles to this precision and decided to look at other options, the first of which was to make precision cuts of plywood panels with beautiful wood veneers. Perhaps a laser cutter could mark and cut wood tiles to the necessary precision.

A chorus of my technically and construction-astute friends warned me against this plan—the plywood edges would respond to the outdoor conditions by curling up or down in response to temperature and moisture changes.

So I went on to evaluate other materials, and re-discovered the appeal of “luxury vinyl tile”, a heavy duty version of vinyl flooring.  Within this category was “marmoleum” a natural mix of linseed oil and other natural ingredients, a modern linoleum.  I found that it was offered in tile plank sizes that could be trimmed into Penrose tile shapes!

I now had a medium, but needed a pattern.  Penrose tiling is not quite as simple as laying the tiles down wherever they fit.  In order to tile the plane, with no overlaps and no gaps, one must follow the “edge matching rules”.  By matching the edges, the tiling that results will ensure that the plane will be perfectly covered.  To help accomplish this, tiles are marked in such a way that adjacent tiles will be placed according to the edge matching rules.

I wanted to make a scale mock-up of the floor pattern.  I tried some of the online Penrose tile patterns, printed them out, and cut multiple copies.  The paper-thin substrate, scissors-cut by hand, were not very successful.  They didn’t lay flat or align well and were easily disturbed by any slight breeze or sneeze.

I discovered an alternative. An Etsy store of homemade wooden toys that included among their catalog of rocking horses and train cars, a set of laser-engraved, wooden Penrose tiles, beautifully crafted, sanded and finished, in either P2 or P3 shapes, all in a handy home-sewn carrying bag!  I ordered one set each from Wooden Giraffe Toys and had them within a few days!  I immediately started making aperiodic five-fold symmetric tilings from them to get a feel of what the floor might look like.

The front of the tiles had the edge-matching rule markings, but the backsides were a solid contrasting color.  Once the pattern was confirmed by the front markings, individual tiles could be flipped to create the visual pattern I sought.

Now that I have a Penrose tile pattern to my liking, I need to figure out how to actually make the tiles and install them.

A pattern of wooden Penrose rhombuses made from the set offered by Wooden Giraffe Toys.
I don’t consider them toys; they are tools!

Stonehenge and Solitaire

My visit to Stonehenge in 1994

When Management Graphics adapted their film recording technology to support motion picture film formats, it was quickly adopted by movie studios to bring special effects from their computer memory images on to film.  There were some problems however, and one of the most serious was the difficulty in obtaining the full brightness range found in typical scenes, especially when they included lights—candle light, desk lamps, car headlights, streetlights.  Any light source, even a glimpse through a window to the bright outdoors, would cause a large flare in the final film frames, washing out detail in the scene.  Our customers complained, and we started down a path to research and solve the problem.

We understood what the fundamental issue was: halation, an effect caused by the glass faceplate of the cathode ray tube used for creating the image.  The bright spot on the phosphor screen was internally reflected at the glass surface which then illuminated the phosphor coating.  If phosphor were black, this would not be a problem, but phosphor coatings are white, as are most materials made of fine powder, and it resulted in this internal reflected light overexposing the film.  In the absence of a black phosphor, there were few other ways to mitigate the halation effect.

An example of halation on a photographic film plate.  The circular haloes and flare are apparent around the street lights in this 1910 image.

One of our customers was incorporating our film recorder into a full workstation system.  Quantel, a company in Newberry, England, had become successful in the early years of digital video and was looking for a way to expand its editing tool offerings into the motion picture market.  Quantel’s engineers understood the halation problem as well, but they didn’t want to rely on our figuring out a solution: they had an aggressive development schedule. 

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An Oscar for Solitaire

I’m occasionally asked about the Academy Award that my colleagues at Management Graphics received. It was during the early days of computer-generated special effects in motion pictures. A product I contributed to, the Solitaire Image Recorder, was selected as a technology advance worthy of the Academy’s Technical Achievement Award.  These awards are delivered in a parallel ceremony to the one we are all familiar with.  It features celebrities of a different kind: nerds.

This is the story of how my friend Rick Keeney ended up on that award stage. It has been adapted from his personal account and is a bit technical, but don’t let those details detract from the overall story line.

Rick Keeney, with the Academy Award for Technical Achievement, 1992.

Invention and Innovation

In the formative days of digital photographic imaging, output back to film was produced using specialized, often hand-built, image recorders that were difficult to align, calibrate, and keep running consistently.  As one of the early companies in the business of building and selling graphics workstations, Management Graphics (MGI) recognized that the drawbacks of the available film recorders were limiting its workstation sales.  MGI kicked off a development effort to build a film recorder that would be a robust and easy-to-use product. 

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Science or Sentiment, Generalized

Career “trophies”, coffee mugs, one of which was created by dye printing technology (depicting our development team), the other a memento commemorating the issue of an arcane patent.

There is a more general problem related to the “what to do with old lab notebooks” that some of us face.  It is what to do with our shoeboxes of photos (virtual digital shoeboxes and real ones).  And written correspondence.  Love letters.  Birthday cards and holiday cards that caught our attention enough that we saved them.  The trophies, actual physical trophies, or the certificates of commendation for a job well done.  Birth and death announcements.  Souvenirs of our travels, the mementos of the high points of our lives. 

All of them carry great meaning to us, invoking a romantic haze of fond memories from those times and places, for those people and events.  Yet those memories are internal to us; they are not shared, even with the persons we may have shared the moment with—at least not exactly. Each of them has his or her own version of those scenes.  And they are not shared in the same way with our children, and certainly not their children.  Our lives are an abstraction to them.  They weren’t even around when the main story was unfolding.

I have come to realize this in the last few years as I have processed the items left behind by my parents after their deaths.  I have a high regard for my father’s technical acumen and his many projects.  Some of them were to gather and archive family history, others documented his personal interests.  He was always an early adopter of technology and embraced digital photography well before I did.  He acquired a large collection of both film and digital pictures, organized in shoeboxes and digital folders.  He worked to digitally scan historic family photos that dated back to the 19th century. 

There is a treasure trove of history here, some even recent enough to overlap with my own, yet I do not find myself compelled to explore it.  And therein lies the problem.  If I am not inspired to carry forward the artifacts of prior generations, why would I expect subsequent generations to propagate mine?

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Science or Sentiment

The title page of my grandfather’s PhD thesis, a thick volume of scientific discovery, each page typewritten in carbon-paper triplicate by my grandmother during their time at Harvard. Interestingly, it was submitted on his (54th) birthday.

“Long before the term ecology became a part of the vocabulary of the scientist, primitive man, looking out over the expanse of blue-green water which characterized his favorite fishing haunt, was probably aware of the fact that notable alterations in the color and clarity of this body of water would occur as the seasons changed.”

The introductory sentence of Theodore Olson’s PhD thesis on algae blooms.

I was witness to my grandparents’ transition to an assisted living apartment from the home they had kept for more than half a century.  Though modest, it was the center of a busy family’s activities, and had accumulated the corresponding mementos through the decades.  It had also collected the technical artifacts of my grandfather’s scientific career, specimens of insects and fish and algae from his ecological and entomologist specialties.  He kept copies of his and his peers’ published works, along with those of his doctoral students, who carried on these disciplines, with the scientific rigor and methods that he taught them over their years in his tutelage.

I was there on the day when he had to empty the ‘wall of books‘ in his home library, which included the dissertations of his students.  There was no space for everything at the new apartment.   A few important reference volumes could be retained, but the others?  What to do with them?  Here were the compiled and distilled understandings of pioneers in biology, acquired through years of painstaking research, building upon the pyramid of human knowledge.  These breakthroughs of their time have now been incorporated into our general understanding of modern biology. 

What should happen to the first-ever photomicrographs of blue-green algae blooming to produce cyanobacterial toxins?  What should become of the tabulated counts of seasonal species of mosquitos that were the vectors of mosquito-borne diseases?  What should be the fate of that first chart correlating taconite processing and asbestos-like fibers in Lake Superior?  All of these new discoveries had been first reported in his research and in the dissertations of his PhD students. 

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When Given Cold Weather…

A flash-frozen soap bubble.

When given lemons, make lemonade. 

When given subzero temperatures, freeze soap bubbles. 

This is one of those things that I have wanted to do for some years.  Living in a place where the temperatures drop to levels well below those in your freezer that solidify water and can preserve slabs of reindeer meat, each year I enjoy a few days of dangerously cold weather.   One can throw a pot of hot water up in the air and it turns into a spectacular cloud of steam and snow; no liquid lands on the ground!  It is also possible to blow soap bubbles that freeze into gossamer ice globes.  They are delicate and beautiful, and I have long wanted to photograph them.

Each year when the outdoor temperatures drop sufficiently, I have tried to do this.  Invariably, there is too much wind—any wind is too much—and the bubbles wander away.  The ones I can catch, usually burst before I can take their picture.

This year however, I had a new strategy.  We recently installed windows on our outdoor screen porch.  The temperature remains cold, but the wind is completely blocked.  I can now make soap bubbles and they won’t get away!

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The Wall of Books

This is adapted from a tribute that my father made at the memorial of his father, Theodore Olson, after whom we are both named, who died in 2002 at the age of 97.  I post it here for the online access of posterity, and to provide a portrayal of the scientific mindset of a family patriarch that influenced not only his students, but his entire family and several generations beyond.  Here is my father’s rendition of our family history.


The start of this story goes back almost 150 years. In about 1860 in Norway, Hans Opjörden left home and went to Oslo. Hans had the misfortune to be the second son in his family, and that meant that his older brother would inherit the family farm. Hans left home and headed off to Oslo, where he went to work in a shipyard building boats. After a while he decided he really wanted to sail on the boats instead of just building them. At this time Norway was a province of Sweden.  Shrewdly, Hans changed his name from Opjörden to Olson (with a Swedish spelling) and got Swedish sailing papers.

He went on several voyages and along the way befriended a shipmate named Peter Magnus Peterson.  We can imagine a conversation between them based on what subsequently happened.  Hans confided that he’d really wanted to be a farmer but had no prospects of getting land—and that being a sailor was not his “dream job”, but was good paying employment. 

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Swedish Candelabras – Finis

It is considered good practice to finish up the old projects before embarking on new ones, but that doesn’t seem to be my way.  The new one gets started and the old one languishes in its nearly complete state, sometimes for years, until I grant amnesty, allowing it to fade into memory.

I had reached the point in the Swedish candelabra project where the challenges of woodworking had been solved, a working prototype had been made, a dozen pieces had been crafted, and all that was left were the trivial details of wiring the electric LED candles.

It turned out that, while not technically challenging, it was incredibly tedious, threading wires, stripping insulation, soldering the bulb contacts, splicing connections and gluing the simulated plastic candlesticks in place.  The first one I assembled took hours.

With eleven more to go, I found lots of excuses to not do them.  Eventually however, when the summer heat advisories provided reason to retreat to the cool workroom in my home, I would complete one, or maybe two, each day.  Eventually I reached the last one, by which time I was proficient– only an hour of assembly!

I can now declare this project complete, and I look forward to displaying the candelabras in our windows when the season shifts once again to long cold nights.  I hope they are seen by the passing neighbors as signs of hope, warmth, welcome, and good cheer, just like the ones we enjoyed in Sweden.

The ancestral home of my great-great-grandfather Sven Johan Lundberg in Mulseryd, Sweden, during a light snowfall last December. If you look closely you will find that each window hosts a welcoming candelabra.

The 15-minute rule, and other covid recommendations

Keeping an eye on my watch while conversing.

Since writing the previous blog entry (“What is my risk?”) I have encountered additional information to refine the risk calculation I outlined.  I found a reference that provides a better value for the relative intensity of aerosol generation between the activities of talking and passive breathing: approximately 10X (compared to my placeholder value of 2).  When this weighting is applied to the social interaction duration histogram, the critical exposure is reduced from four person-intensity-hours to three.  

This does not seem like a large impact on critical exposure but the intensity level associated with talking now requires that all of those short interactions become shorter.  If the critical exposure is 3 hours at level 1 (silent breathing in the same room), and talking is 10 times more intense, then an exposure of 0.3 hours (18 minutes) in conversation with an infectious person will deliver the critical dose of virus-laden aerosols.  This suggests a limit of 15 minutes in any interaction with a stranger: the 15-minute rule.

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