I’m happy to share my latest project, “The RasPi MilliTome: A Manual Sand Slicer for 3D Reconstruction,” which has just been published on Instructables — and even more exciting, it has been featured by their editorial team in the Teachers Section.
Last year, after a series of unsuccessful attempts and acquiring three incubators across two countries, my youngest son’s unwavering determination finally paid off. From a batch of twelve mixed quail eggs, seven hatched successfully, marking the start of our new venture into farm animal husbandry. Currently, we’ve settled for manageable pets like a Siberian hamster, an aquarium, and pond fish, plus several rounds of stick insects, mantises, and spiders, along with their grasshopper and locust food supplies. However, quail care is more demanding. While our sons’ happiness is undoubtedly the most important reward, the delicious eggs produced by our farm breeding activity are equally rewarding for the whole family. It’s particularly satisfying collecting every evening the two expected eggs from the punctual quail hens and admiring their different sizes and pigmentation like beautiful little gems.
If you’re still reading, you’ve probably guessed the main topics of my traditional Easter blog: quail eggs and their shapes and patterns.
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Boundary value problems (BVPs) for ordinary differential equations arise naturally in many areas of physics, engineering, and applied mathematics. Classic examples include the vibration of strings, heat conduction in solids, and quantum mechanical bound states. Unlike initial value problems (IVPs), where all conditions are specified at a single point, BVPs impose constraints at different points of the domain, making them significantly more challenging to solve both analytically and numerically.
The Smoluchowski diffusion equation describes the time evolution of the probability density function (PDF) of a particle undergoing overdamped Brownian motion in a potential energy landscape. It is a central equation in statistical mechanics, soft matter physics, and chemical physics.
In previous posts on this blog I have already introduced the Fourier series and the Fourier transform, following their historical development from Joseph Fourier’s original work on heat conduction to their modern role in physics, engineering, and signal analysis. Rather than repeating that material here, I will take it as a starting point.
When we look at a signal — a sound wave, a vibration, or even a curve drawn by hand — we usually perceive it as a function of time or space. However, very often the most relevant information is not immediately visible in this representation. It is hidden in the frequencies that compose the signal, and in how strongly each of them contributes.
This is precisely the idea behind the Discrete Fourier Transform (DFT): to decompose a discrete signal into a finite sum of harmonic components, each characterized by an amplitude and a phase. Conceptually, the DFT is not a new theory, but a practical bridge between the continuous Fourier framework and the realities of digital data, measurements, and numerical simulations.
Rather than starting from abstract formulas, in this post I adopt a visual and experimental approach. The discussion is supported by an interactive program that allows one to draw an arbitrary signal and explore its harmonic content, and by a practical electronics project where Fourier analysis is applied to real sound and noise signals.
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AGGIORNAMENTO 2: Un primo articolo sulla Rapendula è stato pubblicato l’8 gennaio 2026 [1] sul The European Journal of Physics .
AGGIORNAMENTO1: Nel maggio 2025, il progetto ha ottenuto riconoscimento vincendo il 1° premio nel concorso Instructables All Things Pi. Un grande grazie al team di Instructables!
Qualche giorno fa ho pubblicato un nuovo progetto educativo sul mio sito Instructables. Il dispositivo, che ho battezzato RaPenduLa (dalle iniziali in inglese di RaspPi Pendulum Laboratory), è stato ribattezzato in italiano CAMPO (Computer Analisi Moto Pendolare Oscillante) grazie a un suggerimento di ChatGPT. Ma, come direbbe Shakespeare, ‘What’s in a name? That which we call a rose by any other name would smell as sweet’: il cuore del progetto è infatti una piattaforma video per lo studio delle oscillazioni meccaniche. Utilizzando un Raspberry Pi Zero W2 dotato di modulo fotocamera, il sistema registra ad alta velocità il movimento dei pendoli. Poi, con un’analisi video basata su Python e OpenCV, RaPenduLa è in grado di tracciare il percorso preciso della punta del pendolo, visualizzandone il comportamento oscillatorio in 2D.
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It has become a recurrent habit for me to write a blog on the shape of eggs to wish you a Happy Easter. Not repeating oneself and finding a new interesting topic is a brainstorming exercise of lateral thinking and a systematic search in literature to find an interesting connection. This year, I wanted to explore an idea that has been lurching in my mind for some time for other reasons: billiards.
I used to play snooker from time to time with some old friends. I am a far cry from being even an amateur in the billiard games, but I had a lot of fun verifying the laws of mechanics on a green table. I soon discovered that studying the dynamics of bouncing collision of an ideal cue ball in billiards of different shapes keeps brilliant mathematicians and physicists engaged in recreational academic studies and important theoretical implications.
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UPDATE2: On 8 January 2026, a paper on Rapendula was published in the European Journal of Physics [1].
UPDATE 1: In May 2025, the project achieved recognition by winning first prize in the Instructables contest “All Things Pi.” A big thank you to the Instructables teams!
I have recently published another educational project on my Instructables website. I called the device RaPenduLa for the RaspPi Pendulum Laboratory, and it is a video platform for studying mechanical oscillations. It uses a Raspberry Pi Zero W2 equipped with a camera module to record the motion of pendulums at high speed. The interesting part happens through video analysis: using Python and the fantastic OpenCV library, RaPenduLa can track the precise path of a pendulum’s tip and help visualize its oscillatory behavior in two dimensions.
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My heart leaps up when I behold
A rainbow in the sky:
So was it when my life began;
So is it now I am a man;
So be it when I shall grow old,
Or let me die!
The Child is father of the Man;
And I could wish my days to be
Bound each to each by natural piety.William Wordsworth, March 26, 1802
I couldn’t resist citing the beautiful poetry by Wordsworth about the rainbow to introduce my new Instructable, ‘Explore the Physics of Soap Films with the SoapFilmScope.’ I got the idea for this project by reading an article by Gaulon et al. [1]. The authors describe in detail the use of soap film as an educational aid to explore interesting effects in the fluid dynamics of this system. In particular, they examine the impact of acoustic waves on the unique optical properties of the film. In this Instructable, we have designed a device called the SoapFilmScope to perform these experiments. This tutorial will guide you through the process of creating this device, showcasing the mesmerizing interaction between sound waves and liquid membranes. The SoapFilmScope offers an engaging way to explore the physics of acoustics, light interference, and fluid dynamics.
When a sound wave travels through the tube and vibrates the soap film, it creates dynamic patterns through several fascinating mechanisms:
The device consists of a vertical soap film delicately suspended at the end of a tube obtained from a PVC T-shaped fitting that you can get from any DIY store. By attaching a small inexpensive speaker to it, you can let the film dance to the rhythm of the music.
Sometime ago, I have written about the Lissajous-Bowditch figures. In the same article, it is described how to build a simple device called a kaleidophone to generate Lissajous patterns. Using a small mirror fixed securely to the end of a bent wire on a stable platform and a laser beam from a laser pointer reflects off it, mesmerizing, intertwined spirals of light. The laser beam will appear dancing on the wall of your room. This enchanting display results from two mutually perpendicular harmonic oscillations generated by the vibrations of the elastic wire. These captivating patterns are known as Lissajous-Bowditch figures and are named after the French physicist Jules Antoine Lissajous, who did a detailed study of them (published in his Mémoire sur l’étude optique des mouvements vibratoires, 1857). The American mathematician Nathaniel Bowditch (1773 – 1838) conducted earlier and independent studies on the same curves, and for this reason, the figures are also called Lissajous-Bowditch curves [2].
LB curves result from the combination of two harmonic motions, and therefore, they can be mathematically generated through a parametric representation involving two sinusoidal functions (see Figure and also here). Lissajous invented different mechanical devices reproducing these periodic oscillations consisting of two mirrors attached to two oriented diapasons (or other oscillators) by double reflecting a collimated ray of light on a screen, producing these figures upon oscillations of the diapasons. The diapason can be substituted with elastic wires, speakers, pendulum, or electronic circuits. In the last case, the light is the electron beam of a cathodic tube (or its digital equivalent) of an oscilloscope [3].
The simplest of these devices is the KaleidoPhone, invented (and named) by the British physicist Charles Wheatstone at the beginning of the 19th century [3,4]. The Kaleidophone creates stunning Lissajous patterns and is an excellent example of how science can also be an art form. You can bring the mesmerizing dance of light to life with just a few simple materials and creativity.
In a new Instructable project, I have presented a modern compact version of the kalidophone device fabricated with the help of 3D printing technology and enhanced with a digital camera.
For this last bit of modern technology, the new device is called KaleidoPhoneScope. What makes this little device is the facility to adapt it to record another form of vibrations by adding a speaker and another mirror free to vibrate on its bizarre pattern, recalling SciFi movies promp appear on a free wall (or door) of your studio.
As Christmas approaches, what is the best time to try this device with a traditional song? Here is the result. Activate the captions to see the corresponding frequencies of the tones.
I wish you all to spend a Merry Christmas with your dearest, and I hope to see a peace and
REFERENCES
daniloroccatano.blog 