A Mathematician Paints: Color Charts

Introduction

To prepare for a "plein air" workshop in the desert of California in Borrego Springs I have constructed color charts with the recommended palette of colors.

I am a painter but I was a Mathematician. How does this affect me? More on this in later posts. After I sit on this project for awhile, I will discuss on this blog how I look at painting and art from a Mathematician's point of view: geometries, algebras, perspective, shapes, patterns, groups and their graphs, fractals and chaos in the landscape, golden spiral, dynamic symmetry, etcetera, all with an eye on understanding if a Mathematician's insight can add to the ability to paint. Or at least with an eye to understanding how mathematicss and painting are interwoven in MY life. These posts will include one on the mathematics of color charts!

Color Charts and Karen Ready for the Workshop

Palette

(all Utrecht unless otherwise indicated) Ultramarine Blue, Cerulean Blue (hue, Holbein), Cad Lemon, Cad Yellow Light, Viridian (W&N), Sap Green (W&N), Burnt Sienna (W&N), Yellow Ochre, Cad Orange, Alizarin Crimson (W&N but could be Utrecht). This is the order used for the mixed colors, supposedly for each chart, starting at the left with Ultramarine Blue and ending on the right with Alizarin Crimson

Basic Scheme

Mix each color with the other, with the chart's color predominating. Construct a grid on the support (linen, cotton, paper) using rulers and tape to mark off 10 patches across for each color and 6 rows down for each tint/tone/shade with white added to each mix as we paint the squares toward the bottom row. The top row has pure mixes (no white) and the bottom row shows a bare touch of the mix.
Illustration of grid technique with the Cerulean Blue (hue) chart.

Cerulean Blue Chart with Tape partially off

The yellow ochre chart below was the first chart with penciled grids in which I used the palette knife to mark off edges. I felt this was good practice but it made the chart making all the more time-consuming. So I stopped using spaces between patches for a few charts. Note that in this chart I did not include the YO/YO combination. After this I did use the pure/pure combination so that if the charts were perfectly constructed they would all line up properly in the same order. But in addition, I made a mistake and forgot the Cad Lemon!! So there are only 8 patches. To be redone.....

Lessons Learned

Simplicity: I tried to incorporate too many features at the same time. This is a mistake. Color charts are time-consuming enough and the concentration should be on the immediate goal in mind: the effect of mixing colors.
Tape and Grid: I tried to take a short cut by not taping off a grid which I find time-consuming and error prone. However in the end, when I did do one with tape, it was much easier to paint the little squares so that the total amount of time remained the same. Note that of course, tape has to be applied and removed carefully in the right order. There are many descriptions on how to do this. And information about charts in the literature. Of note would be the famous Richard Schmidt charts.
Drying agent: Initially I added M Graham's walnut oil alkyd to the paint piles hoping this would speed up the drying. It didn't seem to be working. So I stopped using any medium. The charts are still taking a long time to dry. So allow plenty of drying time. (I did try adding Gamlin's solvent free gel to the white for the last two charts. Drying time still to be evaluated.)
Support: paper, linen, cotton pad? I wanted to use my support of choice, linen, in order to mimic as closely as possible what I will use in the field. Perhaps a canvas pad would have been better for this exercise or arches oil paper (see next).
Arches Oil Paper: I ran out of linen so that I did the last chart using Arches Oil Paper. It was much easier to handle. And I am waiting to see how long it takes to dry. I will redo one of my linen charts on this paper to compare.
Palette Knife: I enjoy using a palette knife so its use was natural. At first I attempted to use different palette knife strokes, sometimes with thick paint. This is a mistake. First of all, the paint can be too thick and will not dry fast enough. Also though the roughness of the results interferes with the charts. Light bouncing off the charts makes it hard to see the colors.
Transparency vs opaqueness: One FB comment was that it's useful to draw a black magic marker on the support before adding the patches to see which mixes are transparent (TODO yet).
I used too much paint initially. A little bit will do. See the dabs of paint left over after 1) yellow ochre alone (with leavings from each patch!!) and 2) the two charts: ultramarine and cerulean. They are now in the freezer waiting for a painting. By the end I was saving one row of dabs for each chart.

Yellow Ochre leftovers
Ultramarine Cerulean Blue leftovers
I needed another dimension to indicate warm vs cool. Hence for later charts I reversed the order of the pair, Viridian and Sap Green, since Sap Green is warm and Viridian is cool. Note that there is controversy over which is warmer: Ultramarine blue or Cerulean. The Cerulean hue actually has some white in it and this helps make it cool. But with yellow it's warm. So, which blue should distant mountains use, since we want them to be cooler? Note that in practice I have found the Cerulean hue pushes the mountains back while UB pushes them forward. This needs to be analyzed further.

warm/cool pairs: Cerulean Blue/Ultramarine Blue

Sap Green/Viridian

Cad Yellow Light/Cad Lemon

Burnt Sienna/Yellow Ochre

Cad Orange/Alizarin Crimson

Field use

I intend to take the color charts to the workshop and use them in the field. I like to hold the chart up against the scene to see if the basic color scheme works best with that particular chart. This should be taken with a grain of salt. An additional tool would be color charts representing the standard harmony combinations (e.g., complements, triadic, split-complements). A popular triadic in the south west or in fact in any landscape is: violet, yellow ochre and green, where these are evenly spaced on the color wheel.

Yellow ochre chart for My View

Cadmium Yellow Light Chart (in shade) for My View

Which of the charts for "my view" better encompasses what is seen?

The yellow ochre chart photo has a bright brick pot, which might work very well in a painting.

I feel the distant cool mountain color is missing from the chart so I might take another chart to see if this would help.

Selected Color Charts

Alizarin Crimson

Ultramarine Blue

Viridian

Cadmium Yellow Light

Cadmium Orange

Yellow Ochre Color Chart Repeated - on Arches Oil Paper

My last color chart for this workshop: I decided to repeat the YO chart on Arches Oil Paper, in order to compare it with the original, hoping that it dries in time to be used in the field if desired. Recall that the first YO chart is missing two colors!

Yellow Ochre on Arches Oil Paper

Now the question is: how different is this from the original on linen? It seems more matte so that this should not be used in the field to identify colors if I am painting on linen. But I might do a couple of paper-based paintings anyway. Just to experiment and perhaps to identify what I might do to make this look more like the ones on linen. Perhaps varnish will do the trick.

Original Yellow Ochre on linen

Drying Times

As of 1/21 all charts are dry to the touch EXCEPT for the relatively new Yellow Ochre on Arches Oil Paper , the Cerulean Blue Hue chart and the Sap green chart. Most were not dry to to the touch on the 19th. The Cerulean and the Sap were done on canvas sheets when I ran out of the linen. So these were the latest along with the YO on paper The Sap was completed on the 18th, 3 days ago. Even the earlier very thickly applied colors are dry to the touch on the 21st. Perhaps using the drying mediums did help (first M Graham Walnut Alkyd and the the Gabmlin Solvent-gree gel). I also used the gel for the paper charts - mixed in the white.

I began the charts with Ultramarine Blue on Jan 11, 10 days ago. Every day I would put the charts in the warm, dry Arizona sun in the breeze. The past two days I opted for the garage which in this winter period is chilly at night but warms up in the daytime.

Times (approximate for the first 6):

Ultramarine Blue, Viridian, Yellow Ochre, Cad Yellow Light, Alizarin Crimson, Cadmium Orange, Burnt Sienna dried to touch within 10 days. All on linen 9x12 piece.

Began mixing the white with Gamblin non-solvent gel (faster drying?) at this point

Sap Green on canvas sheet: dried to touch in 4 days

Cad Lemon on paper - dried to touch in 3 days.

Jan 17 -Cerulean blue hue on canvas sheet: still tacky on the 22nd, 5 days later

Jan 20: Yellow Ochre on paper - still tacky on the 22nd, 2 days later

Findings: the canvas pad charts might not dry as fast as the linen charts. Need to experiment with this again someday. Really need to do a test using the color on a pad, paper and linen sheet and test the supports every day. And the same approach: either all thick or all thin, etc.. The paper seems to dry somewhat faster. I need to do this study scientifically comparing apples to apples. It could be that the paint just naturally goes on to the paper more smoothly and thinly.

Notes on Selected Colors

Alizarin Crimson: AC is transparent and has a low value (dark) and this can be seen especially in mixes. AC + Viridian in the right proportion is a favorite cool black. Purples made with ultramarine blue and viridian are quite bright. The mix of AC and Cad lemon yields a rich brick color. In fact the right side of the top row consists of variations of brick. The "orange" that it makes when mixed with the yellows are not as bright as pure orange since AC has some "blue" tone in it, graying down the combination of "red" and "yellow".

Yellow Ochre: yellow ochre can be mixed easily from combinations of Blue/Yellow and Red but in the field we want to save time by not mixing too much. Some feel that a tube yellow ochre is not as vibrant. In any case in the southwest, yellow ochre is a very handy convenience color (as is Burnt Sienna).

Cerulean Blue Hue (Holbein). This color is on the palette since it yields a beautiful sky color. I also liked the effect when mixing this with the other palette colors. The hue has white in its composition which tends to cool it. So this actually works well to push a mountain ridge back for example. This is considered a warm color though since it has a yellowish component.

Selected Grey Scale Versions

It would be interesting to compare some gray scale versions of the charts for values. Ultramarine, Alizarin and Viridian are darker with Cad Yellow Light showing up lighter. It's difficult to compare the values across the charts so that a different presentation is called for here. Or it might be best to take any 'colored' image and produce the grey-scale (black/white, no saturation) version on your own.

Ultramarine Blue Greyscale

Viridian Greyscale

Cadmium Yellow Light Greyscale

Cadmium Orange Greyscale

Alizarin Crimson Greyscale

Opaqueness vs Transparency

When I tried to put in a black line, applying the paint with a palette knife didn't allow the transparency to show through. So in the future - a color chart painted with 1 row with medium (for glazing perhaps) and a brush that will allow the transparency to show through, perhaps in the top row.

New Chart

I came across this Rublen color chart by Stapeliad on wetcanvas.com. This is a good way to see the range for each color on your palette with the transparent version at the bottom. I could have made a transparent version of the colors from our SW palette by using a medium. This was painted on Arches oil paper.

In fact this chart seems similar to the yellow ochre chart I made on the Arches paper in overall feel (arches paper, etc.).

Mathematics

My PhD Mentor, Wilhelm Magnus, specialized in Combinatorial Group Theory and he wrote a popular undergraduate book, Groups and Their Graphs, now out of print and very expensive. I used these graphs while teach Abstract Algebra in College. The graphs buzz around in my head sometime. I haven't seen a specific application to painting here but I think that the categorization of groups fits well with the colors of a color chart. A future project is to map the charts to specific groups and determine the shape and look and feel of the graphs.

A group is by definition a set of objects together with a binary operation that form a closed system: the result of performing the binary operation on two objects will always result in an object belonging to the group. Another necessary component is that there must be an identity element. Each element must have an inverse so that the result of applying the binary operation to an object and its inverse is the identity element. A numeric example would be all the integers with respect to addition (+) with zero (0) as the identity element. Ever integer has an inverse (its negative) such that when you add the two together you get zero (the identity).

For a color chart, I propose that a given palette of colors can be seen to be a group if we define the binary operation as mixing two colors. The result is a color. Here's the tricky part, and to be analyzed further: what would be the identity? Perhaps we can have a color-less oil paint that when mixed with any other makes no (color) change. This could be the identity. However, a color should have an inverse. For any color can we find another that when they are mixed the result is the colorless paint.? This may prove to have some merit, or not.

I like the idea better of establishing a finite set of colors that when mixed with each other (perhaps in a specified ratio) only result in one of the other colors in the set (and not outside). (topic for discussion)

Another possible example to explore: the way we make grays is so logical that it would seem that the behavior of mixing them could be seen as applying to a group of objects. A color and its inverse could yield the neutral grey. Can we say that when mixing a neutral gray and a color the result is still that color (perhaps subdued)? If so this set might have characteristics of a group. Hence for example, orange, blue and grey might form a group with respect to mixing colors if grey is the identity.

Sub-groups are important also. If a subset of a group forms a group itself we call it a subgroup. It could be that a limited palette could be a subgroup of a more extended palette. Need to think about this.

Does looking at colors this way help a painter:? If we can systematize and categorize subsets of colors in such a way that they naturally belong together as a group then we have a different way of looking at colors that might be helpful.

I like thinking about how colors interact in this way with a logical systematic basis.

Search This Blog

Radical Impressionist: A Mathematician Paints