elkemental Force

Art inspired by physics.

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Lissajous Trilogy on Canvas

Lissajous Trilogy on Canvas

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elkement

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Let me show you the genesis of my most involved watercolor pencils drawing so far!

I have constructed 3D Lissajous figures on paper, projecting the three-dimensional world down to two dimensions. But I want my artworks to look three-dimensional, too! So, I am using a canvas stretched on wood.

My experiments with canvas board taught me that the surface should better be smooth. I want to push paint around effortlessly, and colors should remain vibrant.

I am gessoing and sanding the canvas several times:

Photo of the corners of two canvases for painting: One in its original state, the other ones gessoed and sanded. (elkement 2025)
Preparing the canvas: Top canvas in the original state for comparison, gessoed and sanded canvas underneath.

I am not sketching lightly. I am puncturing the canvas with a compass! An ad-hoc innovation is needed to stabilize the drawing surface :-)

A good way of putting scraps of abandoned paintings to good use! And I have an antique quantum field textbook with exactly the right size!

Photo of the backside of a canvas stretched on a frame, pieces of abandoned paintings stuck in between canvas and frame to stabilize the surface.
Photo of the backside of a canvas stretched on a frame, pieces of abandoned paintings and card board stuck in between canvas and frame to stabilize the surface.
Photo of the backside of a canvas stretched on a frame, "filled" with an antique physics textbook to stabilize the surface.

I am starting the graphite pencil construction: Setting up the axis and placing the squares to hold the three two-dimensional projections. Divisions of the circle help me calculate the points on the curves geometrically.

Then I am “projecting up” to the third dimension – using (water)color pencils just to remember what should be connected to what:

Photo of a canvas stretched on a frame, start of a geometrical construction with graphite pencil: Setup of axes, position the three straight-on projections. By elkement 2025.
Photo of a canvas stretched on a frame, start of a geometrical construction with graphite pencils. Work in progress: Complete 2D projections. By elkement 2025.
Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. Work in progress, geometric construction has been completed. By elkement 2025.

It is finally time to add colors, layer by layer. I am touching each “cell” of this painting so many times: With pencil, with a watered brush, with pencil again…

Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. Work in progress, adding a bit of color with pencils. By elkement 2025.
Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. Work in progress, first touch of color, first splash of water. By elkement 2025.
Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. Work in progress - colors start to emerge. By elkement 2025.

Am I done?

Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. Work in progress - adding dark accents, by elkement 2025.

No! I need more colors!

More yellow in particular!

Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. Work in progress, close to completion, by elkement 2025.

Now comes the most meditative part: retracing all the pencil lines with black ballpoint pen!

And here it finally is:

Lissajous Trilogy on canvas, formerly also known as Lissajous 123

Watercolor pencils (and a bit of watercolor markers) on gessoed and sanded 30cmx30m (12inx12in) canvas. Varnished with glossy spray coating!

I’ve also painted the sides of the canvas.

I think this whole process is the most inefficient way to cover a canvas with paint :)

Photo of details of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. By elkement 2025.
Photo of a geometric watercolor pencils drawing on stretched canvas, placed on a coffee table: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. The photo shows the artwork from a slanted angle, displaying als the painted sides of the canvas. By elkement 2025.
Photo of details of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. The photo shows a close-up, demonstrating the sheen of the varnished canvas. By elkement 2025.
Photo of a geometric watercolor pencils drawing on stretched canvas: Three overlapping Lissajous figures defined by combinations of sin(t), sin(2t), sin(3t), and a third "3D" view as an orthographic projection. The lines are used as a tesselation of the drawing surface and colored in the style of stained glass. The painting has been completed as has been varnished. By elkement 2025.
Lissajous Trilogy, formerly known as Lissajous 123 by elkement 2025. Constructing the curve described by x=sin(t), y=sin(2t), z=sin(3t) from its 2D projections.

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Related blog post: The original Lissajous Trilogy 123 plus philosophical thoughts.

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Update, February 2026:

Lissajous Trilogy Canvas Prints

I have finally turned this into canvas prints! Lissajous Trilogy is available in three different sized on stretched canvas in my store – the smallest one equal to the size of the original.

The sides of the original are painted painted with wavy extensions of the construction lines. To achieve a similar effect for the printed version, I have extended the print file with a mirrored and manually distorted version of the drawing!

Mockup of a canvas print created from the drawing Lissajous Trilogy - 3D Lissajous Figures constructed from their 2D projections, colored in the style of stained glass.
Lissajous Trilogy by elkement 2025 – canvas print, available here.

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elkemental Force
elkemental Force
@elkement.art@elkement.art

Art inspired by physics.

515 posts
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2 responses to “Lissajous Trilogy on Canvas”

  1. Bob Avatar
    Bob

    Wonderful!

    Reply
    1. elkement Avatar
      elkement

      Thanks so much, Bob!!

      Reply

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