"… I seem […] only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me". – Isaac Newton.
The motivation for this article stems from my interest in retro-computing connected, on the one hand, to the re-evaluation of my youthful explorations of scientific computing in the BASIC language and, on the other, to the popularity they are having in the amateur sector in recent years and of teaching, single-board microcomputers (single-board computers, such as, for example, the Raspberry Pi). These small computers have considerably more power at a much lower cost than the microcomputers of the 80s. This made it possible to emulate the operating systems of the legendary Commodore home computer models and the MSX extension on these computers.
Therefore, a renewed interest in the BASIC programming language is also occurring. This interest in retro-computing reflects the nostalgia for the great emotions that the development of consumer information technology brought to my generation in the 1970s and 1980s. I remember being so struck by the creativity in using and programming these microcomputers that it redirected my scientific interests and academic career. I have written in other articles about my first programming adventures with Commodore home computers and MSX systems in the late 80s and early 90s and my rediscoveries in computer archaeology. Among the exhibits, I found a small program I used to study acid/base titrations developed in MSX BASIC. Therefore, I took the opportunity to write notes on acid-base balance and titration and thus provide a restored and improved version of my program to students passionate about programming and grappling with this important concept of analytical chemistry.
Another Easter is arriving, and here I am for a new article on old friends: the Eggs. In my blog for Easter 2021, I mentioned squared eggs paraphrasing a sentence attributed to the extraordinary jeweler Peter Carl Fabergé:” This year, your Highness, we will be featuring square eggs.” A hen is unlikely to make a cubic-shaped egg, but we can still transform a cooked egg to get the cuboid shape. If you look for squared eggs on the internet, you will find a tool called the egg cuber that does the magic. Unfortunately, I could not yet try one, but it seems to be doing an excellent job from the reviews. The shape of the egg is not a perfect cube but a cuboid, namely a cube with rounded corners. In my previous article, I anticipated that this shape could be obtained using the superquadric function. Curiouser and curiouser! In this article, I will give a bit of mathematical background and even a source code to play with such a function as my Easter Bunny gift.
In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.
Hugo Rossi. Mathematics Is an Edifice, Not a Toolbox, Notices of the AMS, v. 43, no. 10, October 1996.
Welcome to the third part is the third part of the essential introduction to the FORTRAN programming series. In this part, we will introduce the use of functions and subroutines to structure the programs. Then we use them to make a program to calculate numerical derivatives of mathematical functions.
For Schrödinger, the atom was an oscillating system — like the string of a musical instrument — for which there exist a number of modes of oscillation (fundamentals and overtones) which are interpreted as the atom’s energy states.
Armin Hermann. Werner Heisenberg 1901-1976.
This set of slides is from one of my courses in Computational Chemistry. It covers the one-dimensional solution of the Schrödinger equation using Numerov’s method. The material for this article was mainly taken from the excellent Levin textbook in the reference. If you are interested in more details, please like it and subscribe to my website. This way, I will be motivated to add more of these contents.
In college, before video games, we would amuse our- selves by posing programming exercises. One of the favorites was to write the shortest self-reproducing program. Since this is an exercise divorced from reality, the usual vehicle was FORTRAN. Actually, FORTRAN was the language of choice for the same reason that three-legged races are popular.
Ken Thompson, Communications of the ACM. 27 (8), 761–763, 1984.
This is the second part of the basic introductin to FORTRAN programming series.
Relational operators are used for comparison between variables
In college, before video games, we would amuse our- selves by posing programming exercises. One of the favorites was to write the shortest self-reproducing pro- gram. Since this is an exercise divorced from reality, the usual vehicle was FORTRAN. Actually, FORTRAN was the language of choice for the same reason that three-legged races are popular.
Ken Thompson, Communications of the ACM. 27 (8), 761–763, 1984.
In December of last year, I celebrated the 30th anniversary of my Laurea in Chemistry dissertation. The starting of my thesis dissertation also signed my acquaintance to one of the grannies of the scientific programming languages, FORTRAN. Since then, I have used and (continue to) this language for my research activity by writing several thousands of lines of code. Therefore, I want to share some of my modest programming achievements using this language.
I will concisely introduce this captivating programming language in a series of articles. This is a primer on a programming language with much more to offer, especially in the new versions starting from the FORTRAN 90. Readers interested in deepening their knowledge in FORTRAN can find online many excellent tutorials and discussion groups, as well as plenty of excellent textbooks that have been written.
The FORTRAN language
Fortran (FORmula TRANslation) language was introduced in 1957 and remains the language of choice for most scientific programming. The language was constantly restyled and updated (e.g. Fortran IV, Fortran 77). Recent improvements, recently introduced with the Fortran 90 and 95/2003, include several extensions in more modern languages (e.g. in the C language). Some of the most important features of Fortran 90/95 include recursive subroutines, dynamic storage allocation and pointers, user-defined data structures, modules, and the ability to manipulate entire arrays. Fortran 90 is compatible with Fortran 77 but not the other way around. However, the new Fortran language has evolved in a modern computer language by incorporating constructs from other languages.
Controlling complexity is the essence of computer programming.
Brian W. Kernighan. in Software Tools (with PJ Plauger), 1976.
A C program is a collection of functions. A C function is equivalent to the subroutine in FORTRAN or BASIC and procedures in PASCAL, PERL, or PYTHON programming languages. A portion of the program cannot be executed independently but only as part of another program. The function contains a specific algorithm or a stand-alone procedure. You have already used several library functions in your previous programs. Output commands for printing or reading files (such as printf(), openf()), mathematical functions (sqrt(), cos() are a library or intrinsic functions as well. Other library functions, we can classify as follows
Input/output functions. Input/output on the computer devices (e.g. output to the terminal, printer, hard disk, input from keyboard). It is usually used with #include <stdio.h>;
String manipulation functions. This library contains common operations on strings (e.g., concatenation, length, search, and extraction of substrings). It is usually used with #include <string.h>;
Mathematical functions. Mathematical calculations (e.g. trigonometrics functions, exponentiation, square root extraction). It is usually used with #include <math.h>;
Graphical functions. Function for graphics operations (open a graphical window and canvas) and drawing graphical primitives (e.g. points, line, curves).
Operative system control functions. Operation requiriing allocation of the computer resources or devices (e.g. date and time, allocation of memory). It is usually used with, for example, #include <time.h>;
Data conversion functions. Operation for data conversion (e.g. change characters type, ascii to integer). It is usually used with #include <ctype.h>;
To use these function, you need to use the precompiler instruction #include at the beginning of the program. The compiler use by deafult the standard library #include <stdlib.h>;
You can write your functions, and it is called user-defined functions. The use of function allows the program to structure and makes its organization and reading easier. C language is structured around the use of functions. The main() function is a function that contains calls to other functions, both intrinsic and user-defined functions.
Mais à l’instant même où la gorgée mêlée des miettes du gâteau toucha mon palais, je tressaillis, attentif à ce qui se passait d’extraordinaire en moi. Un plaisir délicieux m’avait envahi, isolé, sans la notion de sa cause.
PROUST Marcel, Du côté de chez Swann.
Ci sono ricordi del passato che rievocano nostalgicamente piacevoli momenti nella nostra vita. Questi preziosi tesori sono, a volte, sepolti nella nostra mente o, come nel mio caso, in quella di dimenticati cristalli di ferrite. Come per dolcetti di Proust, il ritrovamento di queste vestigie ci fa rivivere le emozioni di un passato lontano. I ricordi di cui parlo sono quelle della mia tesi di Laurea in Chimica che dopo essere stata scritta e discussa fu poi dimenticata nella memoria artificiale di obsoleti supporti magnetici degli albori della rivoluzione digitale.
Discussi la mia tesi di laurea il 23 dicembre dell’anno 1992, era l’ultima sessione di laurea di quell’anno. A quell’epoca, non esisteva ancora la laurea triennale che fu introdotta in conformità con il processo di Bologna dall’anno scolastico 2001/2002. Il corso di laurea in chimica era quinquennale e si entrava in tesi nell’ultimo anno. La tesi sperimentale comportava un lavoro originale che doveva essere discusso di fronte a una commissione di laurea composta dai professori del dipartimento, i relatori e i controrelatori (coloro che dovevano leggere la tesi e valutare il lavoro di ricerca e la sua presentazione). Pertanto, la tesi di Laurea (come del resto l’equivalente tesi magistrale) era un’esperienza molto importante nel condizionare la scelta dello studente nell’avviarsi o meno in una carriera accademica. Nel mio caso, la tesi segnò la scelta di intraprendere la carriera dello scienziato e educatore. Scelta che, come gli academici goliardici delle prime università europee, mi ha portato a peregrinare lontano dalla mia alma mater nelle lontane Università del nord Europa. Di fatti, questa prefazione è stata abbozzata a Brema in Germania e completata a Lincoln nel Regno Unito, a pochi chilometri dalla città che diede i natali a Isacco Newton.
Ho recentemente pubblicato nel mio sito su AUTODESK INSTRUCTABLES tre progetti per la microscopia ottica amatoriale e didattica. Sono nati come progetti didattici (STEM) ma possano essere anche utili per applicazioni amatoriali scientifiche. Mio figlio Leonardo (ma anche il resto della famiglia), mi ha aiutato nella creazione della documentazione per questi progetti. In questo articolo riassumo brevemente in italiano la natura edei tre progetti. Le istruzioni dettagliate in inglese per la realizzazione dei progetti possono essere lette sul sito Instructables seguendo i links.
Questo progetto mira a sviluppare un dispositivo che integrato con un microscopio USB economico consenta di scattare foto 3D di piccoli campioni. Il progetto nasce come un’attività educativa di tipo STEM per creare Arduino, la ricostruzione di immagini 3D e la stampa 3D un’attrezzatura utile per alcune entusiasmanti attività scientifiche. Come il mio progetto precedente, è anche l’occasione per condividere attività coinvolgenti ed educative con la mia famiglia e in particolare con mio figli Leonardo che mi ha aiutato a creare questa documentazione e a valutare il dispositivo nel ruolo di un entusiast studente. In questa occasione, anche la mia adorabile moglie ci ha aiutato a realizzare il video dell’assemblaggio dell’attrezzatura. Il roto-microscopio consente di controllare la posizione di un semplice microscopio USB attorno al campione. Questo ci permette di scattare foto accurate da diverse angolazioni e non solo dall’alto lungo la verticale come nei tradizionali microscopi ma anche da direzioni diverse. Questa non è un’idea nuova, poiché esistono microscopi professionali che operano allo stesso modo. Tuttavia, la realizzazione di dispositivo richiede una spesa modesta alla portata di uno studente garantisce molto divertimento nel costruirlo e produce risultati di buona qualità.
By love, that first did prompt me to enquire;
He lent me counsel, and I lent him eyes.
William Shakespeare. Romeo and Juliet. Act II.
Another STEM project is avaialbel here on my AUTODESK Instructable site. We could not help but continue to explore our favourite hobby: microscopy. The interest received in our previous microscopy-related projects has encouraged us to propose other ideas and designs based on further elaborations of both the ROTAMI and the roto-microscope projects. For the latter, Arduino was the microcontroller of choice. In this new device, we decided to take a step further to venture into the use of the fabulous Raspberry PI computer. The results paid back all the e orts; the new ROMIO (I hope Shakespeare’s lover will forgive us for using the illustrious name assonance!) is an XY mobile platform for USB digital microscopes controlled remotely by a RaspPI zero 2 W. In addition to the translation movements, it is possible to adjust the focus of the digital microscope with an additional servo motor. We have developed a simple Python program (called RasPyliet) to control the microscope and automatically collect a series of images for stitching reconstruction.
Moreover, using an additional RaspCamera, you can monitor the device’s correct functioning. The project requires a 3D printer, an inexpensive USB microscope and a Raspberry PI zero W (or higher models) version 2. The project could be used as a STEM project or and affordable replacement for more expensive school equipment for biology projects.
The story of ROMIO and RasPyiet did not end up in a tragedy, but as with every prototype, it still has some known problems and limitations, and there is space for improvement. So we hope you like it, and constructive comments and suggestions are always welcome!