An Averaged Menger Sponge

I’ve been doing a lot more painting than posting-about-painting recently, and got it in my head to line up a lot of Menger objects I’ve made since last summer in one image file and use transparency to roughly average them.  Here’s the result of futzing with that last night:


It’s an imperfect approach since I’m just using some rough napkin math to try (and I am certain fail) to keep the various layers approximately equally contributing to the final image.  It’s 35 layers altogether, I think, a combination of paintings, drawings, sketches, papercraft, and photographs of actual 3D objects carved from soapstone and snow and cork.

I also put together an animated gif that steps rapidly through all of those individual images: it’s by nature a bit flashy so be warned before clicking through: Continue reading “An Averaged Menger Sponge”

Coloring my face


This is a first color pass on top of the brown grisaille self-portrait I started in on last Friday; I gave the entire painting a go with semi-transparent color glazes to try and build color information on top of the values-only underpainting.

I’m not really satisfied with my work here.  The skin tone feels sort of flat, the glazing of the flesh tint I mixed sort of washing out the underpainting more than I expected.  I was imagining a thinner, more transparent glaze, is part of it, but I added about as much linseed oil and solvent as I felt like was doable without getting into seriously ruinous territory and still didn’t get glass-clear glazes.

Having mixed the colors in some cases with white may be part of that; I understand that can add opacity even while otherwise thinning the paint out.

The previous glazing stuff I’ve done has been for abstract Menger sponge stuff (of which, I should do a round-up post on those soon) and being a bit more reckless in just mixing up Neo Megilp and smearing the stuff all over the canvas.  I felt like maybe that wasn’t the way to go here, but I wonder if I’d have been happier with the results?  Or it might have been an awful mess.

Definitely I’m in really out-of-my-depth experimental territory on this.  Which is interesting and worth embracing but it makes it a lot more likely that I’ll do something, not like it, and feel dispirited and let that get to me.

There’s also a feeling of fear in ruining something’s charm by trying to elaborate on it, and all else aside I really did find that initial grisaille charming.  It was sketchy, certainly, but sketches have a lot of attraction for some reason.

Will continue to work on this, and see if I can figure out more of what I’m doing and what I want.  Doing more work in particular on the skin tone to try and create an effect I’m happy with.  I just need patience.

Self-portrait grisaille, from a Huntsville selfie

Painted this last night, based on a selfie I took on my phone in the summer of 2015 when my wife and I were in Huntsville, Alabama for a NASA internship she’d gotten.


This is my third go at self-portraiture in oil paints; I did two last year as well, all based off of photos because I haven’t yet figured out a setup I’m happy with for mirror + lighting + easel to work off my own reflection from.

I’m happier with this so far than I am with my previous two, based respectively off a selfie and off of a delightful blue-hued polaroid candid taken by Tamas Kadar during a meetup at XOXO 2016:

From a selfie at home.

My first oil self-portrait.  It was both pretty exciting to put it together and basically chock full of proportional and tonal problems since I was pretty actively making it all up as I went.

From Tamas’ snapshot.

This was my first experiment in monochrome, and you can see I was playing around with using a palette knife to lay in the white background.  I like the idea with this one but not very much the effect — the more muted blue haze of the original polaroid has a dreamy glow that this totally fails to capture, and again I find the proportional problems with it pretty distracting.

On to the new one, then:

Pencil outlines on canvas.

I started with a detailed pencil sketch on the canvas for this painting. With the previous two I’d done some sort of sketch to start as well, but not with the same care: for the first, just sketching in thinned-out paint with a brush on the canvas which several “starting painting” guides had suggested but which turns out not to work well at all for me; for the second a pencil outline but one I rushed a bit and declined in my desire to get going to stop and fix even when proportions were already seeming off.

This time I took my time, probably an hour or so building it up and reworking lines and redrawing detail bits.  Having done a similar job for a current work-in-progress painting of my cat Freyja was very satisfying and nudged me in the direction of doing so here as well, and it’s starting to feel like a good way for me to work.

I’m still not satisfied with the proportional relationship between the original photo and the drawing, but it’s a lot better and more careful in this outing and I’m happier with the results so far because of that.

Using a monochrome palette.

The grisaille was executed using Burnt Umber mixed with varying proportions of Titanium White, and nothing else.  No black in the mix; it’ll be easy to deepen the darkness of the darkest bits later, and the unmixed brown is already fairly striking on its own, so just fading it up with white was fine for this.  You can note (especially in the hair highlights I added late in the process) how mixing in white dulls the vibrance of the brown, though; I laid down thinned but unmixed Burnt Umber for my hair and eyebrows before doing the rest of the details and it’s the most lively feeling part of this current state.

In the patchwork reading about oil history and theory and practice I’ve done over the last eight months, I’d come across the idea of grisaille painting a few times but it hadn’t clicked for me until recently as I started to read up in more detail on glazing techniques.  Used loosely it can mean just a monochrome painting (whether literally greyscale or using a color as the core pigment), so both this and the previous blue one fall into that bucket, but there’s more specific style and theory ideas tied to the word as well.

The idea of specifically doing a grisaille in grey or neutral colors as an underpainting is the interesting thing to me, now, and where I’m planning to go with this one.

By using an essentially colorless first pass to establish the form of the painting as well as the values (basically, levels of brightness) of the whole composition, you can create a foundation for further work without having to juggle color mixing in the process and all the additional logistical issues and (literal, optical) value judgements that can come with mixing colored pigments.

And with that grisaille laid down, you can return to the dry underpainting and add color with transparent glazes.  That is, not by literally obscuring the underpainting with opaque paint out of the tube but by thinning the new colors with additional linseed oil, mineral spirits, etc. to create a translucent layer of color that lays over and takes on the values of the underlying paint.

This idea of using thin layers of transparent paint to blend optically wasn’t even on my radar for oil painting when I first started; imagine my surprise to find that it’s a fundamental technique in centuries of oil painting!

So I built an easel

When I started painting last summer I bought a cheap wooden tripod easel online, not knowing what I’d need or whether I really wanted to invest too much in what was a brand new, possibly short-lived hobby.

Monday of this week, I took that easel out of the house for the first time, to drive over to my friend Jesse’s place to do art together.  The easel promptly fell into two pieces.

“Jesse”, I said to him, “I would like you to have this easel.”

And so I was without a place to paint, and with a bunch of paintings in progress, and it became urgent to fill my self-imposed need.  And I decided to do it the hard but cheap way: build my own.

Here it is, assembled as of earlier this evening.

Finished easel, with work-in-progress painting of Freyja the cat.

I didn’t design it; this is following very closely on the reasonably detailed plans that have been online for a decade or more care of an artist named Ben Grosser; you can find the plans right here if you’re curious about building one or just want to see what I was working off of.  It’s a project that’s been recommended a number of times over the years on the art discussion site Wet Canvas, which is how I found it.  Thanks, Ben!

But I did build the goddam thing, and let me tell you: I am neither good at nor well prepared for woodworking.  I did a lot of things badly, out of a manic desire to get this thing done ASAP.

Continue reading “So I built an easel”

The Decline And Fall Of Snowmeng


Portland’s snowy hellscape has gone the way of warmer temperatures and more typical rain, and the snowy Menger sponge I built along with it, but I took some pictures while it was still up and while it was in the process of ceasing to be.

My wife had the excellent idea to stick a colored LED lamp in the interior of the sponge to light it at night; the various colors seen in these images are on a cycle that the lamp runs through, and it spent that whole first night slowly easing from one color to the next. Continue reading “The Decline And Fall Of Snowmeng”

Inverting a Menger Sponge

So here’s the question: if a Menger sponge is what you get when you keep removing successive chunks of innards from a cube, what do you get when you keep the innards and throw away the sponge?

You get an inverted Menger sponge, is what.  What does that look like?


Here’s three iterations, illustrated.

A zero-iteration Menger sponge is literally just a cube; you remove nothing, and the inverted sponge is just empty space.

A one-iteration Menger sponge has a tri-axial cross shape removed from it, as if it were a 3x3x3 stack of smaller cubes and you removed the center cube and each of the six cubes adjacent to that center cube on the six respective sides of the original large cube.  The Menger sponge has holes in the middle; the inverted Menger sponge is a blocky 3D cross.

A two-iteration Menger sponge removes the same arrangement of cross-shaped blocks, at one third the scale, from each of it’s remaining smaller cubes; the corresponding inverted Menger sponge gains those, as miniature crosses glued onto the bigger one from the first iteration.

The process continues from there indefinitely, in principle, as the sponge itself gets emptier and emptier, and the inversion gets increasingly bumpy and full of discarded, ever-shrinking cross shapes.


I liked putting this chart together — it started as some sketches last night, see above, because I’ve thought often about the flipside object to my pet fractal — but I was surprised to discover that I don’t actually find the resulting inverted Menger sponge very visually appealing.

It’s got a kind of visual dazzle that I can appreciate, but it doesn’t communicate as clear a sense of shape; all those greebly outcroppings obscure, rather than illuminate, the essential form of the fractal shape, and it’s hard to get a clear sense of where the holes are.

But that may be in significant part an artifact of this flat-shaded isometric approach; that serves the flat-surfaced foundation of the Menger sponge well aesthetically, but a proper 3D model of the inversion with some proper lighting and shadows would probably go a long way toward making it a more interesting specimen to look at and especially to interact with via rotation, etc.

The Abominable Snowmeng, and other winter fractals


It snowed quite a lot in Portland, yesterday and overnight.  About a foot altogether, which for this town is if not historic at least very rare; a typical Portland winter sees no snow at all, or some brief flurries of fat flakes that don’t survive contact with the wet-from-recent-rain ground.  Every two or three years we’ll get a nice blanket of 2 or 3 inches and the city will shut down for a day or two while everyone panics.

This isn’t the first snow we’ve had this winter, so it’s been a weird one on that front already; last time we got some decent coverage, I scraped a Sierpinski Carpet in the driveway with a chunk of scrap 1×6 we had sitting around:


But this was something else, and so it demanded something else: increased dimensionality. Continue reading “The Abominable Snowmeng, and other winter fractals”