Interlock, Part 2

Interlocking pieces serve us well in many ways. In relationships, parts that fit together to make an integral whole keep us together. In furniture, like in relationships, parts and the way they fit are critical in the integrity of the final result. A simple dovetail joint is not as simple as I thought at first. It will come apart unless we engineer it correctly.

And it won't go together if we over-engineer it. Here is an example of a correctly engineered dovetail joint. One degree of freedom is prevented from slipping by making the pegs into wedges that cannot slip out from left to right.

This dovetail joint is engineered correctly. I can imagine knocking it together with a rubber mallet.

Interlocking components are common in everyday life, but sometimes interlock is too complex to actually engineer. M. C. Escher showed interlocking prison bars in Belvedere. It's one of his more interesting impossible figures.

So I did my best to draw some. When I saw them, I knew that they were impossible to actually engineer. But they could exist in real life, because there's nothing to prevent it physically, once it has been made.

It's just not clear to me how they can go together, since assembly becomes a chicken-an-egg problem. This is an example of something that has been over-engineered so much that it cannot be assembled, I think. No, in order to make this: it must be grown.

It is possible, however, to connect four cotter pins so they interlock. This was no problem for me to construct, but it isn't M. C. Escher's impossible prison bars. It shows also that slippage is possible in interlocking figures: it is not necessary that all degrees of freedom are eliminated.

It is heavily interlocking. And you can make several figures that can never really be assembled out of independent pieces. For example, a relative of the rectangular trefoil knot can be constructed from three pieces that interlock.

Like the impossible prison bars, each piece holds the next piece, which holds the next. This one can actually exist physically. And if it did exist, it can be slipped wider and smaller, a bit like a slip knot.

This is exactly the same as the cotter pins, which can be slipped apart in pairs quite easily.

Actually the image of the three interlocking pieces comes from the mutual overlapping slats that I used to construct when I was a kid. Was it my grandfather that showed me? I can't remember.

We used to make these kinds of interlocking models out of popsicle sticks and toothpicks. Since wood can bend, it made the ideal material.

I remember making models that could also remain rigid by tensegrity, a Buckminster Fuller concept. I considered it to be the work of genius.

Eventually, I constructed geodesic models using thick plastic sheets, using an X-Acto knife and a protractor to get all the angles right and the shapes the right size. Then I used gaffer's tape to put the triangles together and complete the geodesic dome. I was probably 13 when I did this.

Most of my models when I was a child were geometric inventions, a celebration of form. But I also understood function. It's just that I chose not to employ it!

I have created an interlocking monogram for Painter 4 (at the end of the post The Miracle of the Paint Can) and also for Painter 5.

I have created an interlocking monogram for my initials here. As usual, an over-under rule is used, alternating pass-over and pass-under along the line of the letter.

I have designed many chop marks over the years, but I haven't really been satisfied with any of them.

Interlock continues to fascinate me, intuitively. It is a brain teaser that incites us to come up with ways to make these objects in real life. I imagine some of the principles used are useful in industrial design.

It turns out that interlock, useful for locks and keys in the traditional sense, doesn't always imply items that touch and constrain each others movements. We have shown this in the first post on Interlock. I will now continue this theme with some interlocking items which do not touch at all.

Some interlocking items have many degrees of freedom, as these atomic rings show. There used to be a depict for an atom, used in the early days of atomic power, that showed three electrons circling a nucleus. This was naive optimism at its most simplistic and iconic. Especially when you consider the inherent dangers and value of nuclear power. I guess they figured that if you gave it an iconic face, a designer-friendly symbol, you could demystify it in a similarly friendly way.

Anyway, here I have shown three interlocking rings. These do not use the over-under rule, but they are nonetheless interlocked in an inseparable way. No two of them are actually interlocked. Remove the third and they fall apart. This is the most powerful and synergistic form of interlock.

Creativity and Painter, Part 4

Painter 5 was a bit of a transition for the core team. John Derry and I were no longer really in charge of the taglines and the copy. But we totally rose to the occasion when it came to the UI and the features. John and I redid the UI to cut down on screen real estate, which required endless work. I implemented a whole host of new brushes.

I could go on and on about the new brushes. When Tom Hedges and Bob Lansdon created the first version of watercolors for Painter 2.0, To added an ability to allocate more than just 32 bits per pixel to either the canvas or even a layer above the canvas. As time went on, we used this feature more and more. For the new water droplet and liquid metal brushes in Painter 5, we allocated another 32 bits per pixel and made it a floating point height field. As we added items to the height field, it could be thresholded, and height-compensated to make it look like there was surface tension, and then rendered into the main 32-bits of the layer, which had the RGB color and an 8-bit alpha mask.

There was plenty of work to do, with these and many other new features. My friend Udo Gauss came out to Aptos during this time frame and I showed him a metaballs implementation, the basis for these new layers. We talked endlessly about how it might be of use to Painter users.

John and I, meanwhile, worked on a monogram-style logotype for Painter 5. John was keen on using a human hand as a primary image, because one of the basic things about Painter is that you use your hands to make art, and Painter is just an amplifier for your talent as a mark-maker and an artist.

Above, you can see an interlocking logo form for Painter 5, with a P and a 5 intertwined that I drew. I got this idea by looking at the royal interlocking monogram chiseled into Danish King Christian IV's sarcophagus in the Roskilde cathedral.

John's take, shown to left, is a 5-pointed star, the numeral 5 overlaying a pentagon. I think the brickwork is another bit of charm in this one. His attention to detail goes on and on. For a quick sketch, it's not bad.

To the right is another example of a joint work page from a notebook. Almost all of the numerals are John's work. The seven-cube design is my work, it looks like.

The really interesting symbol on the page is a 5 with a small p inside it. I think this might have been used in a coin he saw once, perhaps a five pence coin from England.

In the top right, several 5's are shown with varying degrees of thin-line styling, perhaps similar to letters from the Art Deco or Art Nouveau eras. Some of them even have serifs.

I really like the squat 5 in the lower right, with its bold line. This shows the endless doodling we did that often produced interesting results, and sometimes ended up in ad copy, splash screens, and other graphic work we produced.

For every genuine idea we had, really only a small percentage of them actually got into actual use. I think it is often that way with designers in search of a good logotype. I have been to design houses, in particular Landor Associates in San Francisco, and I totally respect their work and the attention to detail and the perception of their client's customers.

With Painter 5, we were trying to think up something to do with the paint can. With Painter 3, we used the paint can in the posters, and the tagline Pour It On was used. With Painter 4, the can was done in mosaics.

To the left is a sheet of John's ideas for the logotype and for the paint can itself. It is really no great wonder that we didn't use the cloudy thunderbolt paint can.

In the upper right you can see John's take on the interlocking monogram concept. Both of us vetoed it. Some of his stylings to the left show a P5 logo with the top of the 5 missing, so it resembles Pb, the atomic symbol for lead.

Umm, no.

John returns to the squat 5 concept again at the bottom. I still like it, but I'm not sure how it can serve with Painter.

So, the question got raised: exactly what was the best symbol for 5? Was there a symbol that meant the most to artists? We decided to sketch out a few and see what stuck in our minds.

To the right is a sketch I did that summarized what I thought might work from a standpoint of straight symbolism. I also drew a few clumsy numbers out as well.

The first and most useful was the human hand. Once again, the mark-making instrument, the center of the artist's expression, was used.

A 5-pointed star also has sticking power. Though, I pointed out, it also symbolizes glitz and fame. Not necessarily good for Painter.

A pentagon wasn't too bad a symbol. But it had military significance, especially since a pentagonal building houses the department of defense here in the US.

A pentagram was an occult symbol. Neither John nor I was necessarily wild about going down that particular path.

The Roman V for 5 was a good, ancient reference to the numeral 5. Very old-time. Maybe.

The dodecahedron was a bit abstruse for the Painter audience, but I had to put it in. In the end, the human hand was chosen as the symbol.

Here is a sketch I did with several references to the number 5, and in many forms. Annotations were applied to it, because we were thinking of using it as an ad design.

Ok, it looks dumb.

When we did an ad design for Painter 5, I actually did the ad myself. It was a hand, with fingers spread, the fingers were on fire, and the numeral 5 was done in liquid metal in the palm.

This was a reference to a scene from my youth where my dad showed us kids the element Mercury. I actually had some in my hand. Had I known it was terribly poisonous, I wouldn't have done that.

The ad, when done, had a kind of illuminati look to it. It was actually my hand, too. Crazy. The ad ran in lots of magazines, but I don't have a copy to show you, I'm afraid. Update: I found it! The artwork for the Painter 5 ad piece with the hand and the burning fingers and the liquid metal 5 can be found in this blog post toward the end.

The work on a monogram something we found to be quite fun, and very much pure design work.

Here, my sketches for monograms are shown to the right. The can is present, with a radiant brilliance coming out of it. Beveled pentagonal tiles are in front of it.

The Albrecht Dürer monogram is alluded to (though he did it with the D below the mid-line of the A).

I did a little John Derry monogram in the middle.

I have no idea what the M5 monograms were getting at. But we had lots of fun in the process.

In the end, we used a brush stroke version of the numeral 5, to match the Painter brush logo.