Sunday, January 21, 2018

A Mathematician Paints: Color Charts


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


(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

  1. 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.
  2. 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.
  3. 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.)
  4. 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).
  5. 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.
  6. 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.
  7. 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). 
  8. 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
  9. Ultramarine Cerulean Blue leftovers
  10. 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 
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 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.).


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.  

Friday, September 2, 2016

A Tale of an Award Winning Painting - "Santa Fe River Turbulence"

The history of this painting began during a Mentoring Program by Albert Handell in June 2015.  I pointed out that the Santa Fe River was running, and so we painted there twice during the week.  The location is on Alameda on the southeast side of the river a block from Delgado Street. What a great location when the water is flowing. I enjoyed sitting and standing, painting and listening to the water babble as it flowed over the rocks, watching the neighborhood children and dogs frolicking in the waves.  My first two "en plein air" studies were during this program.:

"Santa Fe River Flows I", oil, 6x12" (sold)

"Santa Fe River Flows II", oil, 6x12" 
(available at the Marigold Arts Gallery: )

I then returned to the river on my own the next year and painted the larger "Santa Fe River Turbulence".
As I was painting, I was conscious of utilizing a "golden spiral" with a focal point at the golden mean. Fortunately I had chosen a golden ratio for the panel: 10 x 16 (or as close as I could get to this irrational number).  I noticed that the rocks formed a kind of spiral, spiraling to that point and I took advantage of that.
Close-up photo of a section of the river:
Santa Fe River

After painting in the darks with ultramarine blue and Van Dyke Brown (cool and warm) to enforce the pattern and depth I began to place the colors I saw in the water - variations of the primaries, cool and warm with the use of special colors for neutralizing or accenting the painting.  The colors used were: Alizarin Crimson, Cadmium Red Light, Cadmium Yellow Light, Cadmium Yellow Light,
Ultramarine Blue and Cerulean Blue Hue and Titanium white of course from different manufacturers (primarily W&N, Utrecht, Gamblin .  I probably added some secondaries: Viridian Green and SapGreen, Cadmium orange and Cobalt Violet as well as Cobalt Blue. Neutral and accent colors included Gamblin Warm White, Holbein Rose Grey, Gamblin's Portland Grey Dark and Grumbacher's Thalo Yellow Green.

Of note is that I have become freer with the palette knife; if you inspect the small first paintings you can see the knife strokes.  In my efforts to paint solvent-free I find that this helps - fewer brushes to clean but also with resulting cleaner colors. Later in this story for other paintings, my palette changed somewhat for additional river paintings.
Early Stage:

Finishing up:

At this point I added a few sparkles in the river and the trees and some blue sky holes.  And ended up with this:

"Santa Fe River Turbulence", 10x16, oil.

Award presented at the opening show for the 2016 Plein Air Artists of Colorado Annual Show at the Mary Williams Gallery in Boulder, Colorado.

About this time I was invited into the Marigold Arts Gallery on Canyon Road.  They were looking for larger paintings so that I used the Santa Fe River Turbulence to create larger paintings that became part of my "Return to the River Series" at the Marigold gallery.

Note that I changed my palette in the meantime, using primarily Williamsburg oil paints (for the warm and the cool of each primary) along with the transparents and accents mentioned above. 

So, a few small paintings can lead to others, larger and presumably better. "Practice makes perfect" it is said. See additional river paintings at the Purple Sage Gallery ( and the Marigold Arts. 

Final note: Happenstance further inspired me in the river paintings.  During a large Hillary Clinton fund-raiser, hosted by my son, Josh Ginsburg, and other family members, Josh met and became friendly with Vikas Khanna, renowned author, spiritualist, representative of India and celebratory Indian Cuisine chef.  I needed to learn more about him since I do not watch cooking shows on TV so Vikas graciously sent me two books as the mother of his new good friend; one was "Return to the Rivers" about his pilgrimage in India.  This inspiring book resonated with me and, with his permission, I titled my show at the Marigold: "Return to the Rivers". Vikas continues to inspire his countrymen and our leaders with his voluntary work for mothers and children in shelters and has millions of followers on Facebook.

Karen L. Halbert

For a tale of another painting go to the post, Tale of Two Paintings, in March 2016 of this blog.


Information about Holbein's Rose Grey, from the Dick Blick Art Supply site.

 Since I often use the Transparent Oxide Red as a toner, I find that rose grey is harmonious when I wish to tone down the painting in bright areas or to brighten up the painting in duller areas.

00425-3174 — Rose Gray

This color contains the following pigments:

PR101—Red Iron Oxide
Pigment Type
earth, synthetic
Chemical Name
iron oxides (synthetic), iron oxide, silica, alumina, lime, and magnesia or hydrated iron oxide
Chemical Formula
Fe2O2 or Fe2O3 • H2O
Red iron oxide varies in hue and transparency, depending on hydration and slight impurities. Indian Red is a slightly duller, deep brick hue with a bluish undertone. It is very dense and opaque, with excellent tinting strength and covering power. It is dependable when mixing with all other permanent pigments and yields good flesh tints when mixed with Zinc White. It is the synthetic version of PR102, which is a pigment made from earth reds, or natural red iron oxides, and the names applied to PR101 and PR102 often overlap. The synthetic red iron oxides have mostly replaced natural red iron oxides and are brighter, stronger, finer, and more permanent. Indian Red is the highest grade bluish shade. Light Red, English Red, and Venetian Red are yellowish shades. Mars Violet is a dull and subdued bluish or purplish oxide.
Red iron oxide is very lightfast with excellent permanence.
Red iron oxide has no significant hazards.
Natural red iron oxide comes from the mineral ore hematite, called bloodstone by the ancient Greeks from the word hema, meaning blood. It is one of the oldest pigments, has been used by every major civilization, and was an important mineral for medieval alchemists. It was not widely used in artists' materials until the 17th century and was not produced in large quantities until the 18th century.
Alternate Names
Indian Red, Colcothar, English Red, Light Red, Mars Red, Mars Violet, Morelle Salt, Pompeian Red, Indian Red, Red Oxide, Sinopia, Spanish Red, Terra Rosa, Tuscan Red, Venetian Red, Venice Red.

Friday, June 3, 2016

Karen Halbert: Expanded Biography

Karen at the Marigold Arts Exhibition: Return to the Rivers
Karen Halbert is a full time landscape painter, primarily of the Southwest. She was torn away from careers in mathematics and computers to follow her life-long passion: painting. Though she paints in the Southwest, she also captures the images that permeate her dreams – of the powerful ocean waves of the Pacific, home of her childhood.
Driven by the purity of elements of mathematics, found in areas such as dynamic symmetry and chaos theory, she strives to go far beyond her analytical training. The logic of composition and pattern is second nature to Halbert; she is free to experiment with other aspects that help her capture the underlying beauty of the natural world. Her training in the Classical techniques as well as Impressionism serve her well. She can concentrate on capturing the beauty of the landscape surrounding her.
Driven by the light of the southwest, Halbert made a conscious life-style decision to move to Santa Fe. She also wanted to return to her roots in the west. It is here that she has found a true artist’s home. Halbert displays her work throughout the country from Woodstock to the Old Town in Albuquerque as well as in various She is represented by the Marigold Arts Gallery on Canyon Road, Santa Fe and the Purple Sage Gallery in Albuquerque.  You may also view her works on her website,
Halbert is very active in the Plein Air Painters of New Mexico (PAPNM), serving as the volunteer Website Administrator. She is currently working on a major conversion of the website to a state-of-the-art system using her design and computer skills; the work is recalling the many years she spent managing the development of user systems on Wall Street with the NYSE.

Karen: “My paintings go beyond my analytical training and reflect the depth of nature’s magnificent diversity. The logic of composition, edges, values and pattern is second nature to me. I can concentrate and subject's quality, reaching for deeper meaning and the underlying essence of life. Painting on location, ‘en plein air’, enables this subliminal reaction, resulting in paintings that I wish to share.”

Plein Air Artists of Colorado Featured Artist Article of October 2015:
PAAC Article – Karen Halbert
Short Bio: 

Karen strives to transform the beauty of mathematics into her art,
utilizing her knowledge of areas such as dynamic symmetry, fractals
and chaos theory. The “hidden harmony” of Karen's work is shown in
her cloud fractals, wave patterns and stream flows as well as cliff
striations and tessellations. Karen grew up in the West, but moved
East as an adult to attend college and pursue a career as a college
professor of mathematics and computer science, and later as a Wall
Street executive. She eventually settled in Woodstock, New York to
fulfill her life-long dream of being an artist, but ultimately was drawn
back West to the artist-rich town of Santa Fe. Karen continues to use
her computer skills as a volunteer Website Administrator for the Plein
Air Painters of New Mexico.

When did you first become interested in art?
As a child, I loved to draw and paint and I won the high school award
for art (I still have the pin in my jewelry chest). I chose another
passion, mathematics, as a more practical career.

Where do you sell your work? ( galleries, festivals,
I am represented* by the Purple Sage Gallery in Albuquerque and am
planning a featured artist show in December 2015, titled, "Hidden
Harmony". Two of my paintings will be at the New Mexico Art League
in October in the "Biologique" exhibition. This exhibition features art
inspired by nature with concepts such as the "Golden Mean", Fibonacci
sequence, π (Pi), fractals, and mathematical harmony underlying the
works. My works sell through the gallery and exhibitions sponsored by
PAPNM and PAAC as well as through my website,

What is your biggest challenge when painting en plein air?
My biggest challenge is simplifying the scene before me. Allowing my
mind to play with mathematical concepts helps me in the process.

Briefly describe your most interesting or funny plein air

This is really an experience that is an aftermath of plein air
experiences: Six years ago while walking my dog in Santa Fe, I
encountered a woman who took one look at me and immediately
exclaimed, "So, you are a painter!" “What do you mean?,” I
responded. She pointed at the paint on my clothes (I do find that
paint gets all over me especially when I paint outside) and my plein air
hat. As a (plein air) painter herself from Cape Cod, she was
completely aware of the significance! That woman is now my best
friend. Art and painting still remain our favorite topics of conversation
on our daily walks with our dogs, Chili and Caleb, both red standard

Please tell me about an interesting non-– art aspect of
yourself that people might be surprised to know.
Some people might not know that I was a computer programmer, and
then the manager/executive on software projects that are still being
used to drive trading on the floor of the New York Stock Exchange.
Another, perhaps more interesting fact, is that I lived in Honolulu in
high school and return frequently. I have painted in Molokai at the
Leper Colony and Honolulu and plan to travel to the North Shore of
Oahu to paint at the end of this year for a few weeks. I will look for
the hidden harmony in the waves, the cliffs and the clouds.

What is your long-term goal as an artist?
To improve my skills and to impart any knowledge that I have been
acquiring in small classes. Also, to enter more competitions that will
hone my skills.

Any tips on tools, techniques or gear for the budding plein
air artist
Simplify the landscape: look for the big shapes and worry about the
details only at the end, if at all. Keep your equipment light and have it
ready at all times for that moment of inspiration.

What advice do you give an artist just starting out?
Use solvent-free materials; the health hazards of solvents are wellknown.
I recently acquired this as my motto, and I am teaching a class
in solvent-free oil painting in Arizona this winter. Also, work with a
limited palette, a cool and warm of each primary for a more

harmonious painting.

Karen at the Santa Fe River

"Santa Fe River Flows I", 6x12, oil by Karen Halbert

*Addendum. Karen is now also reprented by the Marigold Arts Gallery on Canyon Road in Santa Fe, NM.

Selected Exhibitions – Karen Halbert

September 2016. Mary Williams Fine Arts Gallery, Juried Exhibition, Plein Air Painters of Colorado, Boulder, Colorado. 

May 2016. Marigold Arts Gallery, Return to the Rivers, Canyon Road, Santa Fe, NM.

December 2015 – January 2016. Purple Sage Gallery, Solo Show, Hidden Harmony, Oldtown, Albuquerque, NM.

October 2015. Art Collectors’ Gallery, Juried Exhibition, Plein Air Painters of New Mexico (PAPNM) Annual Members Show, Santa Fe, NM

September 2015. Biologique Juried Exhibition, Albuquerque. An exhibition portraying the connections between art and mathematics.

August 2015. Mary Williams Fine Arts Gallery, Juried Exhibition, Plein Air Painters of Colorado, Boulder, Colorado. 

June 2015. Inart Gallery Juried Exhibition, PAPNM Santa Fe Plein Air Festival

May 2014. Featured Artist, Purple Sage Galeria, Trekking through the Land of Enchantment, Old Town, Albuquerque.

June 13 – July 6, 2014. InArt Gallery Juried Exhibition, PAPNM Annual Plein Air Santa Fe (PASF) Paintout, Santa Fe, NM.

May 2-17, 2014. Gary Kim Gallery Juried Exhibition, PAPNM Annual Members Show, Santa Fe, NM.

October 2013 Millicent Rogers Museum Juried Exhibition, PAPNM Annual Members Show, Taos, NM

June 2013. Gary Kim Gallery, Juried Exhibition, PAPNM Annual Plein Air Santa Fe Paintout, Santa Fe.

May 2012 – current. Purple Sage Galeria, Oldtown, Albuquerque, NM

June 2012. Juried Exhibition, PAPNM Annual Paintout, Ruidoso, NM.

November 2011. Placitas Artists Series 4-Person Juried Exhibition, Placitas, NM

October 2011. Millicent Rogers Museum PAPNM Juried Exhibition, Land and Light, Taos, NM

October 2010. Millicent Rogers Museum PAPNM Juried Exhibition, Spirit of Place, Taos, NM

October 2009. Open Space Juried Exhibition, Little Gems, Albuquerque.

August 2009. Wilder Nightingale Gallery Juried Exhibition, PAPNM Annual Members Show, Taos, NM.

June 2004-2006, Betsy Jacaruso Gallery Exhibition: Luminous Visions in Landscape and Still Life, Red Hook, NY

October 2005. Woodstock Art Association Juried Exhibition, The Beat Goes On, Woodstock, NY.

April 2005. Woodstock Art Association Juried Exhibition, Still Life, Woodstock, NY


Curriculum vitae:
2016 – current. Marigold Arts Gallery, Canyon Road, Santa Fe.
2010-current. Purple Sage Gallery, Oldtown, Albuquerque.
2005-current. Moved to Santa Fe from Woodstock to study with oil painting masters, Roger Williams, Doug Higgins and Albert Handell (and others). Volunteer Website Administrator for the Plein Air Painters of New Mexico. Continued to participate in juried exhibitions.  Frequently take painting trips with friends to places such as the Grand Canyon, Hawaii and the Tetons. But I concentrate on painting trips to Ghost Ranch and Abiquiu and to Taos as well as  day trips around the environs of Santa Fe.
2003-2005. Studied with master oil painter, Keith Gunderson. Woodstock, NY.
2003. Retired and Moved full-time to Woodstock, NY.
2002-2005. Studied with watercolorist, Betsy Jacaruso, Woodstock, NY.
December 2001. Began serious training to become an artist.
2001 – 2003. SIAC/NYSE Vice President in charge of Trading Engines, managing over 100 people.
1997-2001. SIAC/NYSE. Managing Director of the Display Book, the premier application used by the Specialists on the floor of the NYSE.
1996-1997. SIAC/NYSE Computer Scientist/Manager of a New Display Book, managing dozens of consultants to update the systems on the NYSE.
1993-1995. SIAC/NYSE. Manager of the Specialists’ Display Book.
1986-1992. SIAC/NYSE. Computer Programming Consultant.
1983-1986. Philon, Compiler Design Computer Software Startup Company. Programmer and Manager.
1973-1982. College of Mount Saint Vincent, Associate Professor of Mathematics and Computer Science, Riverdale, New York. Taught Beginner classes with references to Artistic terms such as Groups and their Graphs and th Fibonnacci Series. Taught advanced classes in Abstract Algebra with references to Geometric transformations between structures (groups) and to patterns such as tessellations of the plane. Courses taught included Calculus, Complex Analysis and Abstract Algebra as well as introductory courses in Mathematics and Computers to non-math majors.
1969-1973. Graduate Program in Mathematics, Courant Institute of Mathematical Sciences, NYU. PhD in Combinatorial Group Theory. Dissertation. Symplectic Groups (Geometric Transformations of Hyper-space.) Taught in a teachers’ training program and taught undergraduate courses at NYU while a graduate student.
1967-1969. US Peace Corps. Chimbote, Peru. La Escuela Normal Marianista de Chimbote. Taught ’New Math’ to Elementary School teachers in Spanish.
1964-1966. Computer Programmer. Columbia University, Underwater Acoustics Research Laboratory in Dobbs Ferry, NY.
1960-1964. Undergraduate program at NYU majoring in Mathematics. Full NYU scholarship and NY State Regents Scholarship.
1956-1960. High School. Roosevelt High School, Honolulu, Hawaii. National Merit Finalist. Art Award.
1950-1955. Seattle, Washington. Attended Elementary School in Ballard and Catherine Blaine Junior High School in Magnolia.
1942-1950. Vancouver,Washington. Oldest of six children.

Defining moments:
May 2016. Return to the Rivers, exhibition at the Marigold Arts Gallery.  My son Joshua met a world renowned author and chef, Vikas , at a major political event.  One of his books is titled “Return to the River”. While reading the book into the middle of the night I realized that I have always been drawn to rivers (and oceans).  I was very moved by Khanna’s activities, supporting women and children throughout the world. He has raised himself up from poverty to become beloved by the Dalai Lama, Obama, Hillary Clinton and now my son and by millions watching him on his cooking programs. Khanna also donates dinners to womens’ shelters. Meeting him has opened up a new world for Joshua. I hope to record part of this world in my art. Hence the title of my new exhibit at the Marigold Arts Gallery.
February 2016. While teaching an oil painting class, I found that digging deeper into the techniques of painting and the theory helped me beter undersand what makes a great painting. I have tried to utilize my findings in my new works.
October 2005. Moved to Santa Fe to return to my western roots and to paint the wondrous New Mexico light and landscape.
October 2003. Retired early so that I could dedicate myself to a new career painting full-time. Moved from Manhattan to our summer home in Woodstock, NY to be surrounded by the beauty of the landscape in another artist-rich community.  I was especially inspired by scenes of the Hudson River and the painters of the Hudson River School legacy.
October 2001. Attended an executive program in San Diego, flying there in spite of security concerns. A question asked was: what did I do besides work.  This made me consider my life. It was then that I reminded myself how much art meant ot me when I was younger and how much I ued it for examples in my Mathematics’ classes.  I also realized that an important part of my career involved the presentation of data. I began to teach myself watercolor (with the help of a paint-by-numbers watercolor set from my son for Christmas.)
September 11, 2001. At the NYSE I managed the turnover of the software systems to support the opening of the NYSE on Monday, September 17. Then we implemented the system to be highly compliant with Security measures. This was a life-changing period.
1982. Changed from the academic world to the corporate world, transitioning through a start-up company.
1960-64. Chose careers in Mathematics over Art as more practical, though both fields are passions. I took many art courses (and religion and philosophy) as well as the requisite mathematics and physics courses.
1973. Only child, Joshua, born. He attended excellent schools (Fieldston in Riverdale, NY and Carnegie Mellon), studied to be an architect and is an executive for a large Manhattan architectural firm designing and promoting web-based systems; he’s become a computer ‘nerd’ like his mom while his mom became an art ‘nerd’. Josh designed my website,, so that I can update it as needed (often). We are working jointly on a project to upgrade the website to a state-of-the art implementation. I enjoy visiting him and his young family, now in San Diego, frequently, tying the visits into California coast painting trips.
1966. Joined the Peace Corps, leaving a corporate job in computers. Teaching there transformed what I wanted to do. I decided to continue in graduate studies afterwards so that I could teach Mathematics at the undergraduate level.
1955. Moved to Honolulu from Seatlle. I became totally immersed in the Hawaiian culture, while working within an academic challenging environment; the high school I attended was the last ‘english standard’ class in Honolulu. To get into the school required a test. Even today I enjoy returning to one of my second ‘home’ to paint and absorb the beautiful landscape. My high school friends opened my eyes to a world in which prejudice exists; I vowed to spend my life working to correct this and to trying to find beauty around us and peace.

Early childhood. The excellent junior high school I attended in Seattle opened up the world for me, showing me that I could escape a life of poverty and pursue any dreams I might have. Even today I enjoy returning to my childhood home to visit my close relatives and to view the beautiful scenery and to contemplate painting it (as I did with watercolors ten years ago).