Expanded Penrose Tessellations with Robots

Believe it or not we had two more snow days this week! On Thursday I broke my snowblower clearing out 15” or wet, heavy stuff. Thursday night was had more snow and Friday it turned to rain, and then more snow for a slushy and mess. Oy! Well the weekend came and some sunshine, and a chance to get caught up on my rest. And the Olympics are on. I never really get into the summer games very much, but I do enjoy the winter games. In any event, I’m sure everyone is looking forward to spring.

My origami friends Brian and Beth are going to be getting together at a maker event next week, where they will have access to a large cutting machine. Brian asked me if I could provide a cutter-ready file of the crease pattern for one of my Penrose tessellations. When I worked on this before, folding by hand, I did the first three expansions, creation patterns with 10, 35 and 70 cells. With the prospect of the machine doing the scoring, larger tessellations become feasible. I created CP’s for the next two expansions, which come out to 105 and 175 tiles. These numbers are really interesting, because they are all multiples of 5 and 7. 2 x 5 =10, 5 x 7 =35, 2 x 5 x 7 =70, 3 x 5 x 7 =105, and 5 x 5 x 7 =175. You’d expect five, but it’s very strange how seven figures prominently as well.

As for the CPs, I was able to dispense with all the landmarks and only include creases that appear in the final model. This ought to make the folding go much faster as well as providing a cleaner appearance. In addition, I shortened all the line segments so that the intersections don’t get scored, to avoid weakening the paper. Lastly, I color coded the creases so that the facets are blue, the ridges between the are red, and the creases for collapsing the intersections are grey. This was fairly time consuming, an unexpected but fun little project. Good for waiting for the snow to melt and watching the Olympics. Having worked the CP out to 175 I think I’m done with this for a while. If you’re an origami person with access to a cutting machine and are interested in trying one of the patterns, please feel free to contact me. Meanwhile, I’m looking forward to seeing how Brian and Beth’s experiment comes out.

Let’s Go to the Movies

The cold and snow continue. Last Wednesday we had another foot of snow, but this time is was wet and heavy and when night came it turned icy. We’re running out of places to put the snow. Cars were getting stuck everywhere. My SUV was parked in the street, and I couldn’t just roll over the snow like I usually do; I had to actually clear out under the front end and the tires with a shovel. Meanwhile my next door neighbor decided gunning his engine and spinning his wheels was the way to go. Shaw’nuff a wheel finally caught pavement his car when flying sideways off his driveway and he had to get towed out. Last night we had another few inches to make everything pretty and treacherous again.

This weekend was the ICS school musical. Michelle was one of the performers. She sang in a bunch of numbers and a had a speaking part in the finale. Lizzy graduated last year but came back to help on lights, while Jeannie ran the video recording and again I played in the band. This year the format was back to a musical review and the show included songs from a whole lotta movies from over the years. I played mostly sax, but learned the banjo for Rainbow Connection. I was able to borrow a banjo from Erik. He told me it used to be his grandfather’s and was made in the 1920’s. It played great but was a real pain to keep it in tune. Once I got the hang of it I used it on a couple other tunes, Yankee Doodle Dandy and Supercalifragilisticexpialidocious.

Of course two rehearsals were cancelled because of snow days, so it was a bit tight pulling it all together. The closing number was a Wizard of Oz medley. It required some tornado music and there was no score for any. Joanne is the piano player and she’s very good, but she’s not much on improvising, so I showed what I would do on piano if asked to come up with tornado music on the spot. I started with the wicked witch riff a few times, then held down the pedal and banged thunderously on clusters of low notes, and then gradually began working my way up and down the keyboard until it became whooshing, whirling glissandos. Meanwhile Matt the drummer was whacking away tempestuously as well. Over on synthesizer Mike was riffling thru his presets. “I have seashore. No? How about helicopter?” (Mike btw is an excellent piano player and does a solo jazz/lounge act a local bar on Fridays. He’s also the husband of the play’s director, so she was giving him some particularly displeased looks.) As Mike got to barking dogs I finished with a gentle, consonant major arpeggio. Joanne regarded me dubiously. However a few minutes later when the director roared at us “Do I have my tornado music yet?!?” , Joanne looked wide-eyed terrified for a moment and then launched into pretty much an exact rendition of my storm etude. By showtime Mike decided to ditch the sound effects and add a bass line instead.

It’s always amazing how the show comes together out of the chaos of the rehearsals. We two shows on Saturday and both performances went really well. It’s really great to see the kids who have been at it a few years getting bigger and taking on leading roles. Some of them have really amazing voices. And of course the kids really love it. Lizzy and Michelle will be singing show tunes for weeks.

This is the fourth one of these shows I’ve done, and it gets easier to learn the songs each time. Now I’m back in playing shape compared to two years ago when I started. Between these school shows, my rock band and my own practicing I must have learned over 200 songs in the last two years. There used to be a time when I could only hold 3 hours or so of music in my head before I’d start forgetting stuff. Now it seems I have much more memory capacity. Let me see if I can remember the playlist. Act I: Maybe, It’s the Hard Knock Life, I Think I’m Gonna Like It Here, The Good Ship Lollypop, Moon River, Swinging on a Star, Get Happy, Talk to the Animals, High Hopes, We Need a Little Christmas, I Just Can’t Wait to Be King, and Time Warp. Intermission. Act II: That’s Entertainment (Entr’acte), Pure Imagination, The Candy Man, The Age of Aquarius, Supercalifragilisticexpialidocious, Yankee Doodle Boy, Hail Holy Queen (a real showstopper), Ghostbusters, Rainbow Connection, Over the Rainbow, Tornado Music*, Ding Dong the Witch is Dead, Munchkin Land, Lullaby League/Lollipop Guild, Follow the Yellow Brick Road/We’re Off to See the Wizard, and Hooray for Hollywood! (curtain calls).

Still Rock’n’Roll to Me

The other night I took Jeannie and the girls to see Billy Joel at Madison Square for her birthday. Billy is one of Jeannie’s all-time faves and it was Michelle’s first arena concert, so they were all very excited. Billy’s grown on me over the years too. Last time I saw him was in the 80’s at the height of his pop phase and at the time I thought he was pretty cheesy. He spent a few years not doing much and somehow emerged as one of the all-time greats of rock. Now he’s not exactly touring, but doing one show a month at the Garden, supposedly indefinitely until he stops selling out. I might go back again in the summer.

He’s never sounded better. Since he’s put on weight his voice has more power and resonance, and a soulfulness it never had before. Billy’s piano playing keeps on improving too. He reminds me of Bud Powell, with hands like bear paws flying around while his fingers hardly seem to move. We had great seats BTW, directly behind the stage looking down at the band. I could see Billy’s hands quite clearly and I can tell you he doesn’t always follow the way the music is in the book!

Billy has a great band too. He’s got nine players and between then cover all the sounds from all his different styles and really nail the sound of the record. Horns, guitars, synths, drums, percussion, everything. This group has been together a long time and have a really good collective vibe and are really tight.

Yet at the same time the set was pretty loose. Billy kept on throwing in improvisations, bits of other songs, changing the lyrics to little jokes (“It’s a pretty good crowd for a snow day”), and extemporaneous raps between songs. He was celebrating the 50th anniversary of the Beatles’ coming to America, and threw in part or most of When I’m Sixty-Four, The Night Before, and A Hard Day’s Night, as well as Let It Snow and Layla as intros/interludes. At one point he looked at the next song on the set list (I could read it off the teleprompter) and played a different song entirely.

As far as the actual set goes, Billy played alot of deep tracks mixed in with the big hits, and skipped all of his songs I don’t like. Highlights include Miami 2017, Vienna, Zanzibar, Allentown, Movin’ Out, Captain Jack, New York State of Mind, Always a Woman, River of Dreams, and Scenes From an Italian Restaurant. I checked the set list from his January show and he did about half the same songs and half other stuff. The encores were Big Shot, Still Rock and Roll to Me, You May Be Right, and Only the Good Die Young.

Great show. Happy birthday honey!

Super Winter

January was very, very cold. Some people have told me it was the coldest on records in 20 years. It was down to 3 or 5 degrees a lot of mornings, and even on warm days it only got into the teens. It takes a lot of energy to endure the extreme cold and by the end it feels like a miracle to survive. Luckily no on in the family got sick, although pleanty of people were out at the office.

Last week two of the guys in our band called in sick for practice, the lead singer and one of the guitarists. So Mike the bassist and I split the vocals. Some of our songs worked better as a quartet than others, so toward the end of session we just started calling songs to jam. I called two from the Infinigon days that went over so well we added them to our set. One is Burnin’ for You by Blue Öyster Cult. The other is Money by Pink Floyd. I had heard Mike jamming on the opening riff to warm up once before so I knew he knew it.

February came and started with a really warm weekend. It was up into the 40’s on Saturday and the 50’s on Sunday. Everything melted, and I even started up my Mustang and let it idle in the driveway for 20 minutes or so. I thought of taking for a drive, but the roads were all full of slush and salt, so I waited.

Today it’s heavy snow again. Already to 6” or so since I woke up. And in the middle of if the tree people finally showed up to take the logs off our yard and cur down the stunp. They’re at it now with a giant truck-crane-claw and a chainsaw. I’ll bet the lawn underneath is totally trashed but at this rate it’ll be quite a while before I can see it.

Cover Up

Great news! my book, Origami Animal Sculptures has gone to print. Last week was a flurry of even-more-minor corrections and finally approvals. The publisher sent my comps of the final cover including the back and the return flaps for the dust jackets. I finally got to read the endorsement blurbs from fellow origami artists John Montroll and Marc Kirschenbaum. I sent out the requests months ago. Thanks very much for your kind words, John and Marc. Also the back cover looks really great with thumbnails of the models taken from Bob’s photos.