Translucent Heart

Last year I’ve started drawing mathematical functions (relevant to physics), using traditional techniques of descriptive geometry.

The very first test was an attempt to capture the three-dimensional Lissajous figure built from sin(t)/sin(2t)/sin(3t).

Lissajous in a Box (Work in progress). Traditional descriptive geometry. Axonometric projection of the 3D Lissajous figure described by x=sin(t),y=sin(2t),z=sin(3t), as created from the 2D views sin(t)/sin(2t) (bottom) and sin(2t)/sin(3t) (top right)
Lissajous in a Box 2024 (Work in progress), geometric drawing by elkement 2024. 3D Lissajous figure(s), axonometry, constructed from two of the three 2D orthographic projections which are simple Lissajous figures… in turn constructed from divisions of circles. Traditional drawing, descriptive geometry. Pencil, watercolor pencil, ballpoint.

Here is a blog post on the history of Lissajous in a Box!

I’ve returned to it several times, and I ran out of names. I called this version Lissajous Trilogy 123 – created on technical drawing paper which looks rather “cold” and grey.

Lissajous Trilogy 123, by elkement, 2024. 3D Lissajous figure, axonometry. From two of the three 2D orthographic projections, which are simple Lissajous figures. Traditional drawing, descriptive geometry. Pencil, watercolor pencil, ballpoint.
Lissajous Trilogy 123, by elkement, 2024. 3D Lissajous figure, axonometry. Using a different point of view and different arrangement of the three views on the paper. Each of the 2D views can be translated in the direction of the projection (z-axis and x-axis). Graphite pencil, watercolor pencils and ballpoint pens.

I wanted to put more emphasis on the construction of the 2D projections from “first principles” – dividing circles to “calculate trigonometric functions geometrically”.

And I wanted to document the Making Of.

So, here is the next version of Lissajous 123, now I call it Translucent Heart!

Translucent Heart by elkement 2025. Mathematical art, geometrical construction on paper. 3D Lissajous figures as an orthographic projection constructed from 2D projections. Series of photo thumbnails showing the construction step-by-step.
Translucent Heart by elkement 2025 – Making Of

In contrast to the first tests, I’ve drawn on – thick and textured – watercolor paper. This type of paper is so not suitable for technical drawing, but I wanted to rise to the challenge!

This is the scanned drawing color-corrected and made “warmer” by reducing the color temperature. This heart should not be too cold!

Translucent Heart by elkement 2025. Mathematical art, geometrical construction on paper. 3D Lissajous figures as an orthographic projection constructed from 2D projections.
Translucent Heart by elkement 2025. Geometrical construction of the parametric curve x=sin(t),y=sin(2t),z=sin(3t). Graphite pencil, watercolor pencils, ballpoint pen on watercolor paper.

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Edit – voice from the future, May 2025: I changed my mind about the coolness of the heart. The print shops listed below now have the original, “cool” version!)

Translucent Heart by elkement 2025. Mathematical art, geometrical construction on paper. 3D Lissajous figures as an orthographic projection constructed from 2D projections. Watercolor pencils on watercolor paper.
Translucent Heart by elkement 2025. Scanned again in May 2025, not color-corrected.

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

Art inspired by physics.

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