elkement

Physics Art Notebooks

... from original geometrical drawings on black paper.

Original - A4, colored pencils on black paper - printed to an A5 notebook (70 sheets, dotted)

Two different drawings on front and back side, in this case:

1) Theory of the gyroscope, Poinsot's cones annotated wih their German names 2) Special relativity, hyperboloid-shaped energy-momentum relation.

Three different combinations of two images available:

Osculating Circles

Colored pencils on black paper, scanned.

Traditional descriptive geometry construction.

The osculating circle to a curve matches its slope and its curvature. For an ellipse (or conic section in general), you can construct it exactly.

Here, I let a hypothetical particle move on a meandering path. I zoom in on one squiggle - which I happen to match one half of an ellipse (yellow) exactly.

Turning the ellipse so that it lies flat in the drawing plane, I can construct the osculating circle (red)… which appears as an ellipse viewed from any other direction.

I draw every ellipse freehand, but guided by its osculating circles. So, also the ellipses representing the "true" osculating circle have their own osculating circles.

New physics art drawing and print!

An illustration highlighting both the geometry of the motion of a spinning top in physics, as well as the descriptive geometry construction used to depict it.

Colored pencils (Polychromos, Albrecht Dürer) of black paper.

When a spinning top rotates, even when no external forces are acting (e.g. when it is supported in its center of gravity), its instantaneous axis of rotation is gradually changing. The spinning top spins about its own symmetry axis, and the symmetry axis itself rotates.

This motion can be visualized using three cones. The red and the blue one are fixed. Their symmetry axis represents the constant vector of angular momentum. The small yellow cones is rolling along the surface of the red one. The symmetry axis of the yellow cone symbolizes the axis of the actual spinning top, and it traces out the surface of the blue cone. The intersection of the red and the yellow cone is tangent to both and the instantaneous axis of rotation.

This image is for an elongated object with an equally elongated ellipsoid of inertia.

Geometry of orthographic projection I used to depict the cones: I draw the top view (circles) and side view (mostly triangles) first, and then coonstruct the main view by intersecting the projection rays. Most of the lines are for auxillary constructions, such as finding the intersections of the ellipses and the generatrix that is part of the outline of the cones.

"Dreaming of Better Times"

(Invert Art) My sketch of antique agricultural technology: an angular gearbox, once used for driving power tools with a tractor. The wheel in the back was part of the setup. Inverted art: I've converted a photo of mine to grey scale and inverted it; this has been my reference.

Aharonov–Bohm Effect

... a famous, puzzling effect in quantum mechanics. Two beams of electron (electron waves) interfere, causing diffraction patterns. If the electrons pass by a solenoid, the pattern is shifted - even though the magnetic field is zero everywhere outside this coil. What is not zero is the so-called vector potential, the field you can use mathematically to "build up" the well known electric and magnetic fields.

The vector potential has been considered more of a mathematical device and not "the real field" - but this effect shows it has some life of its own. The effect is also called the simplest exmple of topology having an impact on physics (the space with the solenoid "removed" is not simply connected.)

Colored pencils (Albrecht Dürer, Polychromos) on black paper, orthographic projection of the diffraction pattern and a torus-shaped solenoid. The diffraction pattern is exact, but not based on the realistic parameters for this experiment. There would be many more maxima within a very small angle. I also "popped out" the little solenoid that would be tiny in relation to the distance between it and the screen in the experiment.

Available as a fine art print or art card on INPRNT:

Another hyperboloid, now the two-part version:

Mass Shell

When you spin a hyperbola ("boomerang") you get either a "vase" / "power-plant cooling tower" (see my last posts) or you get these two "shells" - depending on the axis of rotation.

These hyperboloid represents the so-called mass shell in physics - the relativistic relation between energy and momentum. I have removed one dimension of momentum from the 4D spacetime as the space I can use has only 3 dimensions.

When the momentum is zero - the particle under consideration sitting still - the energy turns into the iconic mc2. If the mass is zero, the hyperboloid turns into the yellow light cone. The shell with negative energies "gives rise" to antiparticles. This is not a tangible interpretation, it is more like a conceptual shorthand. Historically, antiparticles "showed up theoretically" first in the first relativistically correct treatment of electron states by Dirac… where he interpreted the unwanted negative energies and the energies of positive holes in a sea of states filled with electrons. The troubles with these interpretations go away if you stop thinking about the the theory describing single particles but actually a field that can "pop out" any number of particles…. as the combination of quantum mechanics (uncertainty of energy) and special relativity ("mass is equivalent to energy") demands. When you plough through this calculation in detail, you can still see that negative energy state "create" antiparticles.

Colored pencils on black paper, traditional descriptive geometry.

New blog post:

Seems that potential email followers of my Wordpress blog are currently not able to confirm their subscription! Probably we should all go back to bookmarks or RSS :)

Latest blog post, subscribe info at the bottom:

Just a drawing of about 100 years old scissors!

Created with colored pencils (orange, white, black) and black paper.

Postal Scales

My next technical still life: Originally drawn with brown colored pencil on pale green cardboard; then digitally inverted.

The original drawing:

Reference has been this public domain museum exhibit photo:

Magnetic Compass - Technical Still Life Practice

I know it looks eerie, but this is not AI :-)

I have drawn this freehand on paper, using an inverted photo as a reference:

Colored pencil on some pale green cardboard (office supply left over from a more analog era).

Public domain reference photo - museum exhibit:

Temperature Waves

Watercolor on watercolor paper, glued to a stretched canvas and varnished!

Heat equation, definition of diffusity, and temperature distribution in the four seasons (Northern hemisphere).

Energy is stored in summer - and available to be utilized by heat pump in winter.

Physics background:

"Circles to Lines (2026)"

... is done! It is finally also a canvas print!! Originally also created on canvas ... which has been a challenge as I gessoed and sanded this canvas, and watercolors do not stick to this surface at all!

As usual: Traditional descriptive geometry - "how we did 3D before software" :) This is about stereographic projection (circles through the North Pole onto lines), displayed using orthographic projection.

I took the photo for the print after varnishing the original canvas. Varnishing has been necessary to make the watercolor pigments adhere to the canvas. The upside of using this difficult drawing surface: Colors stay way more vibrant!

Available in three sizes; the smallest one is the same size as the original drawing / painting:

I have written something about drawing with code!

New project: Literally draw with code in the same way I use pencil, compass, and ruler, following the rules of descriptive geometry.

Circles to Lines - still work in prgress

"Circles to Lines", work in progress.

Via stereographic projection, circles on a sphere containing the North Pole are projected onto lines in the equatorial plane. Graphite pencil construction and watercolors on gessoed and sanded canvas - a difficult surface to use with watercolors as the water is not absorbed at all. I am using the top view and side view to construct the "3D" view from a different perspective, using the techniques of traditional descriptive geometry. So, technically this is "orthographic projection of stereographic projection". Here is a earlier photo, from the construction stage: