#eulerian

[fuckyeahfluiddynamics]

Tracking Ice Floes

To understand why some sea ice melts and other sea ice survives, researchers tracked millions of floes over decades.  (Image credit: D. Cantelli; research credit: P. Taylor et al.; via Eos) Read the full article

[blake447]

One more lol. Sierpinski Eulerian circuit, colored based on distance along the circuit. Ended up fairly visually interesting

[henrysglock]

What is it with the Duffers and Numbers

Because I'm me and I can't rest until I've parsed out number shit with dates in Stranger Things...I decided to use OEIS to see if there was an kind of pattern in important dates. Our important dates being: 1959 -- Creel Murders 1971 -- Willel Birth Year 1979 -- HNL Massacre 1983 -- Mothergate 1985 -- Keygate 1986 -- The Rifts

From here, I decided to find duration differences between events. March 1959 -> (?) 1971 = 12 ≤ x ≤ 13 years (?) 1971 -> Sept. 1979 = 8 ≤ x ≤ 9 years Sept. 1979 -> Nov. 1983 = 4 < x < 5 years Nov. 1983 -> July 1985 = 1 < x < 2 years July 1985 -> March 1986 = 0 < x < 1 year

This is where OEIS came in handy.

If we round down, we get 0, 1, 4, 8, 12.

This sequence includes all relevant ages for El and the Creels:

Henry and Alice are 12 and 15 respectively when the Creel murders happen. Henry's Virginia is 36. Henry's Victor is 40.

Edward and Virginia, are also presumably 12 and 15 when their Creel murders happen. Edward's Victor is listed as being 35. Edward's Alice has no age listed.

Born in 1947, Henward were 24 when El was born.

El and Henward are 8 and 32 respectively when the first gate opens.

El and Henward are 12 and 36 respectively when Mothergate opens.

El is 15 or close to it when Vecward, now 39, opens the Rifts.

The Mindflayer, while not being a gate-opening event, occurred in '84, which also appears in the sequence.

That's really freaky on its own.

However, If we round up, we get: 1, 2, 5, 9, 13. This sequence is known as the Euler Path:

What makes this so interesting is a) it's a well known pattern (if you're a math nerd you've heard of it before. Suzie would absolutely know this pattern), and b) it has Implications™

Essentially, the Euler Path/Circuit is the longest single, non-overlapping path between two points.

Being a biology nerd myself, my favorite Stranger Things science connection is this:

The Eulerian path is routinely used, nowadays, to reconstruct genomic sequences for ancestry tracking/taxonomic tracking. It's essentially a highly-accurate, DNA-based version of what Dustin did with D'art in ST2. It's an algorithmic puzzle-solving strategy.

The most relevant connection is actually tied to the definition of a Eulerian Path/Cycle, and that is:

Timelines, The Missing Creel Door, the 5-Room Puzzle.

As we've seen in Em's post here, the very structure of the Creel house changes in the show:

A founding puzzle related to the Euler Paths theory is the 5-Room Puzzle.

Now, our house has six rooms, including the foyer/hallways, which makes it slightly different from the 5-Room Puzzle. I was able to find a variety of solutions to each, and there was one pattern that emerged:

They're almost the same, but based on the odd-evenness of the door assignments...they're distinctly different. Each path variation in Edward's house begins in the chess room. Each path variation in Henry's house begins in Victor's study. Both end in this odd, unseen console/kitchen area.

They start differently, separated by a wall. Edward's house has the doorway between those starting rooms, Henry's does not. It doesn't matter. They both end up in the same room.

I'm working on finalizing a look at the loops and cycles version of these paths, and I'm fairly sure there's a pattern in there too, but I have to nail down a couple of other details before I go posting them.

[captainhowell]

For @eulerian-circus

Thank you for your patience.💛

It took quite long for me to finish this work. To understand what it was like: I was need a practice to draw rocks,there is so many redraws in this work that it's scary.🫣In the end it's nice, tho.✨

[boycritter]

she hits all my edges till im a eulerian cycle

[lesbianslovebts]

Me: I'm gonna write.

Also me: researching Eulerian graphs for half an hour

[abalidoth]

OH FUCK OFF AD

fuck you assholes that graph isn't Eulerian

[kitwallace]

Circle designs

From a Mastodon toot "This is how a real data scientist drinks coffee"

The image is by Javier Jaén. It looks very real but it must be computer-generated. I wondered if I could make it real and used my work on Eulerian circuits to create a spiral-printed version (sans handles). Intersecting circles create a Eulerian circuit since every intersection is even, but the path is not so obvious. The code in JavaScript computes the intersections and the arcs between intersections, constructs a graph and uses the Hierholzer algorithm to find a path.

This is the Gcode generated from Fottery

and here printed in white PLA

The cup profile is adapted to make it easier to print.

Next step is to make it in ceramic.

Printed in a stoneware clay on my Eazao Zero. Not as prefect as the computer-constructed image, just as useless as a cup but it is a real object .

[normally0]

The Bridges of Königsberg Reimagined In the heart of Königsberg, the riverside town crisscrossed by winding waterways, the seven bridges have stood as symbols of connection and challenge for centuries. While the town’s inhabitants speculated about the possibility of crossing each bridge exactly once without retracing their steps, Euler's mathematical proof dashed the hopes of such a journey. Yet, history does not always rest on proofs—it often beckons for new perspectives. The story begins with the geographical map of Königsberg, where the landmasses labeled A, B, C, and D are separated by flowing rivers. Each bridge—a, b, c, d, e, f, g—links the islands and shores, forming an intricate web of connectivity. Yet, from a bird's-eye view, the arrangement resists simplicity, posing a tantalizing challenge for mathematicians and wanderers alike. Enter the mind of a modern thinker, gazing upon Königsberg not with frustration but with the clarity of geometric innovation. The bridges and landmasses are transposed into a hexagonal grid—a geometric canvas of interconnected hexagons. Each hexagon becomes a node, and the bridges transform into bold, red lines that traverse this modular plane. In this hexagonal world: A sits at the centre, radiating connections to B, C, and D. The red bridges carve precise, logical paths, their traversal no longer constrained by the physicality of a river but by the elegance of the hexagonal symmetry. As the hexagonal plane grows in complexity, the thinker tilts the map. The flat representation of Königsberg begins to rise, folding into a three-dimensional lattice. Hexagons morph into prisms, each landmass gaining height and depth. The bridges, once mere lines, stretch into spatial connectors that weave through this layered structure. From this elevated vantage: The impossibility of the Eulerian path dissolves into potential, as movement between layers introduces new pathways and possibilities. The rivers, now shadows upon the planes, recede into history, leaving a lattice of infinite connectivity. The thinker finds inspiration in the Giant’s Causeway, whose hexagonal basalt columns mirror the grid of Königsberg’s reimagining. Nature, in its chaotic order, provides the blueprint for a timeless solution. Just as the columns of the Causeway rise and fall in a rhythmic dance, so too do the landmasses of Königsberg shift and connect in this new vision. Through the interplay of flat grids and rising lattices, a new kind of journey unfolds. It is no longer about crossing each bridge just once, but about embracing the limitless potential of geometric transformation. The walk becomes a metaphor—not of limitation, but of exploration. The thinker, standing on this new Königsberg, sees not a town divided by rivers but a boundless landscape of connections. The bridges no longer constrain but liberate, leading to a realm where mathematics, nature, and imagination converge.

[hackvertiser]

Affiliation et ROI, le divorce?

La promesse originelle de l'affiliation était de garantir à l'annonceur un ROI fixe, la rémunération de l'éditeur étant prélevée directement sur la marge lorsqu'une transaction était finalisée. Le rêve.

Et ce rêve a permis aux affiliés et aux affilieurs, ainsi qu'aux plateformes tiers de confiance, de prospérer depuis la création de l’affiliation sur internet par Amazon à la fin des années 90.

Comme tout système vertueux, il a été victime de son succès. Aujourd'hui, nous sommes toujours dans un système basé sur la performance, mais les calculs se complexifient et de nombreux biais entrent en jeu. Explications.

Prenons un marchand dont le panier moyen se situe aux environs de 100€ et sa marge brute à 30€. IL estime qu’il peut rétribuer un apporteur d’affaires (l’affilié) 10€, soit 10% de l’achat finalisé par son client. Sur le papier, tout le monde est gagnant, le marchand peut laisser la magie de l’affiliation opérer, tout ce qu’il reversera aux affiliés ne lui coutera qu’une part de sa marge qu’il aura défini à l’avance en fonction de ses propres besoins. Mais ce tableau idéal sera bientôt obscurci par de multiples écueils. Tentons une analyse chronologique, étape par étape :

Recruter des affiliés Alors qu’ils n’étaient qu’une poignée au début des années 2000, les marchands opérant un programme d’affiliation sont plusieurs milliers aujourd’hui et doivent se démarquer pour attirer des éditeurs, ce qui passe souvent par des rémunérations attractives et par un travail de recrutement intensif qu’il est souvent tentant de confier à une agence tierce.

Fournir des « assets » Bannières au standard IAB, kits HTML pour les e-mails, bases produits en XML ou CSV, liens texte, codes promo, etc. Tout un arsenal de véhicules publicitaires à créer en interne et à fournir aux affiliés en respectant leurs spécifications qui ne sont pas toutes standard. Un coût supplémentaire à inclure dans le calcul de marge mais qui s’avère indispensable.

Gérer les conversions en attente Retours du client, paiement refusé ou non parvenu (chèques…), voire paiements frauduleux, etc. Il est indispensable de veiller à ce que les conversions soient réelles avant d’attribuer la commission finale aux affiliés. Par chance, la plupart des plateformes permettent de mettre en place un délai d’attente avant que le paiement des gains ne soit confirmé. Mais cela suppose une routine de validation à suivre régulièrement (au-delà du délai les conversions se valident automatiquement). Conséquence pour les affiliés qui surveillent également leurs marges, ils ne pourront réellement investir e leur côté qu’une fois les premières validations effectuées afin d’éviter toute mauvaise surprise, surtout s’ils achètent à d’autres acteurs du trafic ou des espaces publicitaires (« arbitrage »). Pour ceux-là, il convient de limiter le temps d’attente de validation des gains si l’on veut les rassurer sur leur revenu réel et non juste « potentiel ».

Modèles d’attribution Et voilà la grande question qui hante tous les open spaces de l’E-Commerce mondial depuis des années et qui brouille les pistes entre ROI garanti et affiliation.  Mais de quoi s’agit-il ? L’affiliation n’est qu’un levier parmi d’autres : achats de mots clés sur les moteurs de recherche (SEM), référencement organique (SEO), réseaux sociaux, CRM, partenariats divers. Et aujourd’hui lorsqu’un CMO (Chief Marketing Officer) en charge d’étudier l’apport de chacun des canaux consulte ses statistiques internes (fournies par un outil analytique, comme Google Analytics, Eulerian, Piano ou Piwik par exemple), il constate des écarts entre ce que lui montre la plateforme et ces statistiques interne. Par exemple il va voir dans GA4 que telle vente provient de Facebook alors que cette même vente est attribuée par la plateforme d’affiliation à un affilié lambda. Que faire ? Rémunérer l’affilié qui a certainement contribué à faire venir l’acheteur ou lui dénier toute implication et refuser de lui rétrocéder une partie du CA généré ? Bien que des modèles d’attribution/contribution alternatifs existent, permettant de valoriser d’autres « touchpoints », voire l’ensemble de la chaine de valeur, les annonceurs, fidèles à leur dogme ROIste, restent attachés à la règle du « Last click », soit le dernier clic avant la conversion.

Les effets (pervers) d’aubaine Cette règle du « Last Click » a une autre conséquence : c’est le dernier qui a parlé qui a gagné. Autrement dit, l’affilié (ou le levier) qui a fait découvrir le site ou le produit voit sa commission « écrasée » par le clic d’un levier « bas de funnel » (retargeting, code promo, cash-back…), ce qui finit par le dissuader de relayer le programme d’affiliation… Au final, l’annonceur se retrouve avec un réseau d’affiliés qui parviennent à s’approprier des conversions alors que les achats étaient déjà initiés par les clients finaux. CA incrémental : proche du néant.

Dégradation de la fiabilité du tracking Le tracking des conversions se faisait essentiellement via une technologie qui repose sur le cookie-tiers (de la plateforme). Cette méthode n’est plus fonctionnelle depuis longtemps sur certains navigateurs comme Safari ou Firefox. Et bientôt sur Chrome. Les plateformes ont des parades, mais s’agissant de données personnelles, les internautes ont aussi à leur disposition de nombreuses parades, notamment les ad blockers. Même si la plupart des sites e-commerce se mettent en conformité par rapport au RGPD à reculons, en déposant par exemple des cookies sans un consentement « libre et éclairé », ce qui a pour avantage de maintenir le tracking cookie actif, ceux qui mettent en place une CMP (Consent Management Platform) permettent aux utilisateurs de bloquer les cookies de tracking des plateformes d’affiliation. Résultat : des conversions générées par les affiliés mais pas trackées, donc pas rémunérées, ce qui peut apparaitre comme un gain pour l’annonceur mais qui ne fait que renforcer la position des affiliés les moins qualitatifs et faire fuir les plus pertinents…

Ces différents facteurs contribuent à décorréler le ROI réel (difficilement valorisable avec les outils actuels) et les couts marketing de l’affiliation. Pourtant le modèle continue à séduire car il reste basé sur la performance et l’annonceur dispose toujours de cette sécurité unique : pouvoir supprimer des conversions en attente de validation en cas d’erreur ou de fraude (ou de mauvaise volonté). Le risque dans l’affiliation (commission sur lead ou vente) repose encore et toujours sur l’affilié mais celui-ci n’entend plus se contenter de prendre son lien d’affilié et le diffuser auprès de son audience, il doit aussi s’y retrouver financièrement faute de quoi il se détournera définitivement du programme d’affiliation.

La solution passe par de l’expertise car la plateforme d’affiliation n’offre qu’une boite à outils (tracking, facturation…), encore faut-il pouvoir s’en servir : connaitre le réseau des affiliés (forces, faiblesses…), adapter son site, mettre à disposition du matériel marketing pertinent, implémenter un tracking fiable (si possible en server-to-server), mettre ne place une grille de rémunération progressive, etc.

Personnellement, je recommande de toujours ramener les commissions des affiliés au volume de clic généré afin de déterminer un CPC moyen et le comparer au CPC payé par exemple pour des liens sponsorisés sur les moteurs de recherche. Si le eCPC est au-dessus, il faut s’assurer que ce trafic est véritablement qualifié et au contraire, s’il est trop bas, anticiper un départ de l’affilié et lui proposer une hausse de rémunération en échange d’une mise en avant.

Cette vision d’un cout ramené au clic, présent chez de nombreux acteurs dont Google AdWords, permet d’anticiper également une évolution du CPA (Cost Per Action) vers le CPC, quitte à renverser la charge du risque, de l’affilié vers l’annonceur. Mais cette inversion permet à l’annonceur de bénéficier de volumes plus significatifs et toujours contrôlés lorsque le budget est défini à l’avance (volume de clics, CPC fixe). A noter cependant que les internautes ont tendance à ignorer de plus en plus les bannières et autres liens publicitaires (lorsqu’ils ne sont tout simplement pas bloqués par des applications anti-pub), il est donc vital pour l’annonceur de communiquer sur des offres réellement attractives, soit avec un visuel particulièrement léché, soit avec une remise ou un code promo ou avantage client réellement intéressant, soit avec une information suscitant la curiosité de l’internaute.  Au final, la publicité repose encore en grande partie sur la créativité et l’innovation, y compris dans l’affiliation !

[a9saga]

I got a 5/10 on a discrete math quiz on Tuesday. I was really surprised when I saw the grade on Blackboard yesterday because I was quite sure I was correct. And I was. It was a single question. I will explain.

In graph theory, a path connects multiple vertices by shared edges. By "vertices", I mean points, and by "edges", I mean a line connecting them. Length of a path is the number of edges that goes from one vertex to another. Vertices are necessary for any graph, but technically, edges are not. A graph can have all vertices, or basically all points, and not a single edge connecting any of them. That's called an empty graph. And if a graph does have edges, they don't all have to meet each other, and not every vertex has to be connected to any others by an edge. This means there isn't necessarily a path from one vertex to any other on a graph. Also worth noting, the "degree" of a vertex is how many edges offshoot from it to other vertices. But anyway.

A circuit, or a cycle, is a path of a graph which loops back to the vertex it started from. Or if you want to use the vocabulary, its starting vertex is also its terminal vertex. Because there isn't necessarily a path from any vertex to another, there isn't a necessarily a circuit for any one point either.

An Eulerian path is a path of a graph that crosses each edge of the graph exactly once. And if that path is a circuit, it is an Eulerian circuit. Not every Eulerian path is an Eulerian circuit. If the last edge does not connect its terminal vertex to its original, it is an Eulerian path, but it is not a circuit. So for the quiz, we were given the prompt of drawing a graph with 6 vertices, 7 edges, which contained an Eulerian path but not an Eulerian circuit. I drew something that looked like this

Enjoy my shitty little MS paint recreation btw. The green are the vertices. I drew those first. I drew and erased several edges before I got to this, but there are seven of them. And if you were to start at vertex 4, you could go to vertex 1, but there is no other edge connecting another vertex to 4. From 1 you can take the edge to 5, 5 to 6, 6 to 1 again, 1 to 2, 2 to 3, 3 to 6. There are actually a couple of ways you can travel between 1, 5, 6 and 3. But there's one. It's Eulerian. It crosses all 7 edges once, but whichever way you take, you cannot return to 4 without going over its only edge a second time.

When I got my quiz back today, I received a comment on it that is Eulerian, but the explanation that my professor was looking for is that it has exactly two vertices of odd degree. 4 has a degree of 1 and 6 has a degree of 3. The other three vertices have degrees 2 and 4. My explanation of the path being Eulerian was very literal, rather than me identifying properties. And to be honest, I did not study examples of Eulerian shits before the quiz. I honestly thought the prompt was going to be something else entirely. I was looking over some coding shit before the quiz because I'm not a comp sci student but the course is designed for them. I hadn't thought about that property of an Eulerian path in days. I'm not mad I had points deducted for giving a very literal, to the textbook definition answer. I see that I could have described why it is Eulerian without stating the path outright. I do think I deserved more than half credit. I just wanted to get that off my chest.

[blake447]

A Chaotic way of drawing an Eulerian path along Sierpinski's triangle

Been posting a bit about generating sequences for various fractals that draw them utilizing absolute heading turtle graphics. Here's a time lapse of one of said sequences (10x speed) drawing it in perhaps one of the most chaotic methods I think I've seen.

That'll be enough on this topic for now unless I find something really, really interesting but yeah, this has been on my todo list for awhile now

[holmoris]

describing anything involving vertex transforms as 'eulerian' is the graphics world version of the black and white 'has this ever happened to you?' clip at the beginning of the informercial trying to sell you on some type of reversible matrix operation

i love in computer graphics papers or presentations when they compare their findings to previous inferior research in the same field. get dunked on Eisenberger & Cremers you stupid fucking idiots

[maacsatara]

Simulation and Dynamics: Fluid Simulation and Particle Systems

Simulation and dynamics are crucial fields in computer graphics and animation that allow artists and developers to create realistic representations of physical phenomena such as fluids, smoke, fire, hair, and cloth. Among these, fluid simulation and particle systems stand out as powerful techniques used to bring lifelike motion and effects to digital environments. These simulations are fundamental to visual effects (VFX), video games, virtual reality (VR), and scientific visualization. For those looking to master these advanced techniques, studying at the best VFX institute in Pune can provide the necessary training and skills. This article delves into fluid simulation and particle systems, exploring their principles, applications, and impact on the digital world.

Fluid Simulation: Bringing Realistic Liquids to Life

Fluid simulation refers to the mathematical modeling of liquids and gases to recreate their behavior in a digital environment. This technique is essential for creating realistic effects like water, smoke, fire, and other fluid dynamics that react naturally to forces such as gravity, wind, and pressure.

**Key Concepts in Fluid Simulation:**

1. **Navier-Stokes Equations:** Fluid simulations are based on the Navier-Stokes equations, which describe the motion of fluid substances. These equations are a set of nonlinear partial differential equations that govern the conservation of mass, momentum, and energy within a fluid. Solving these equations accurately is the key to achieving realistic fluid simulations.

2. **Grid-Based Methods:** One common approach to fluid simulation is the grid-based method, which divides the simulation space into a 3D grid of cells. Each cell stores information about the fluid’s properties, such as velocity, pressure, and density. The simulation calculates the interactions between these cells over time to produce realistic fluid motion. The most popular grid-based method is the "Eulerian" approach, which tracks the fluid’s velocity field at fixed points in space.

3. **Particle-Based Methods:** Another approach is particle-based simulation, such as Smoothed Particle Hydrodynamics (SPH). In this method, fluids are represented as a collection of particles that interact with each other based on physical laws. Each particle carries properties like mass, position, and velocity, and their interactions determine the fluid's behavior. Particle-based methods are particularly effective for simulating free-surface flows, such as splashing water.

4. **Hybrid Methods:** Modern fluid simulations often combine grid-based and particle-based methods to achieve higher accuracy and stability. Hybrid methods can capture the strengths of both approaches, allowing for detailed surface representation and realistic interaction with solid objects.

**Applications of Fluid Simulation:**

Fluid simulation is widely used in various fields, including:

- **Visual Effects (VFX) in Film and Television:** Realistic fluid simulations are used to create stunning water scenes, raging fires, smoke, and explosions in movies and TV shows. For example, the water effects in "Pirates of the Caribbean" and the fire in "Game of Thrones" were achieved using sophisticated fluid simulation techniques.

- **Video Games:** In video games, fluid simulation is used to create dynamic environments that react to player actions, such as splashing water or smoke from explosions. Although real-time fluid simulation is computationally intensive, advancements in graphics hardware and algorithms have made it possible to achieve convincing fluid effects in modern games.

- **Scientific Visualization:** Fluid simulations are also used in scientific research to visualize complex fluid dynamics, such as weather patterns, ocean currents, and aerodynamics. These simulations help researchers understand natural phenomena and make data-driven decisions.

Particle Systems: Creating Complex Effects with Simple Elements

Particle systems are another powerful tool in computer graphics, used to simulate a wide range of natural phenomena like fire, smoke, rain, dust, and magical effects. A particle system consists of a large number of small, simple particles that collectively form complex visual effects.

**Key Concepts in Particle Systems:**

1. **Emitters:** The emitter is the source that generates particles in a particle system. Emitters can have different shapes, such as points, lines, or surfaces, and can control properties like emission rate, direction, and speed. For instance, a point emitter might simulate a spark, while a surface emitter could simulate rain falling on the ground.

2. **Particle Attributes:** Each particle in a system has attributes like position, velocity, color, size, and lifespan. These attributes define the particle’s behavior and appearance. Over time, particles may change color, fade out, or follow specific motion patterns based on predefined rules or dynamics.

3. **Forces and Dynamics:** Forces such as gravity, wind, turbulence, and drag affect the motion of particles in a system. By applying these forces, developers can create realistic effects that mimic real-world phenomena. For example, particles in a smoke simulation might rise and disperse as they interact with turbulence and wind forces.

4. **Shading and Rendering:** The appearance of particles is controlled by shaders and rendering techniques. Shaders define how particles interact with light, color, and transparency, enabling the creation of different effects like glowing embers, misty fog, or glittering stars.

**Applications of Particle Systems:**

Particle systems are widely used across various industries:

- **Visual Effects (VFX):** In movies and TV shows, particle systems are used to create dynamic effects such as explosions, fire, smoke, and magical spells. For instance, the dust and debris in battle scenes or the shimmering particles in a magic spell are often created using particle systems.

- **Video Games:** Particle systems are used to create interactive and immersive environments in video games. Effects like fire, rain, snow, and smoke are simulated in real-time using optimized particle systems, enhancing the gameplay experience.

- **Virtual Reality (VR) and Augmented Reality (AR):** Particle systems are also used to create realistic and interactive effects in VR and AR applications, such as fireballs in a VR game or confetti in an AR experience.

#### The Future of Simulation and Dynamics

As technology continues to evolve, the future of simulation and dynamics looks promising. Advances in hardware, such as GPUs, and the development of more efficient algorithms are pushing the boundaries of what is possible in real-time simulation. Techniques like deep learning and machine learning are also being explored to predict and simulate complex dynamics more efficiently.

Furthermore, the integration of simulation tools into game engines and 3D software packages like Blender, Houdini, and Unreal Engine is making these technologies more accessible to artists, designers, and developers. This democratization of technology is opening new doors for creativity, allowing for more realistic and interactive experiences in digital media.

Conclusion

Simulation and dynamics, particularly fluid simulation and particle systems, play a crucial role in creating realistic and compelling visual effects in digital media. These techniques allow artists and developers to simulate complex natural phenomena and bring digital worlds to life. Learning these techniques at a reputable VFX institute in Pune can help aspiring artists master the skills required to create such effects. As technology advances, the potential for more accurate and efficient simulations continues to grow, paving the way for more immersive and visually stunning experiences in movies, games, and beyond.

[priyaohia]

Euler’s method is not the just one concept named after him. There are many other concepts named after him; Euler’s constant, Euler line of triangle, Euler’s equation of motion, Eulerian graphs, to name a few. He has worked on a variety of area including astronomy, logarithms, calculus, the motion of the moon and plenty more. It is not surprising that he is such a high figure of influence in the world of mathematics. His concepts made mathematical applications so understandable for everyone today.

[diogo-beloto]

Fluid Mechanics: Topic 10.1 - Lagrangian vs Eulerian descriptions of flow