fractal

When a heavy atomic nucleus splits into two fragments, an invisible quantum thread remains between them. This thread is entanglement: the state of one fragment is instantly linked to the state of the other, as if they were still a single whole. For the first time, physicists have precisely calculated how long and strong such a thread can be, tracing the fission process step by step.

The night sky looks like a random scattering of stars. But zoom out to enormous distances, and the chaos disappears. Galaxies gather into long filaments and flat walls, with colossal voids gaping between them — cosmic voids. This structure is called the cosmic web.

The night sky looks like a random scattering of stars. But zoom out to enormous distances, and the chaos disappears. Galaxies gather into long filaments and flat walls, with colossal voids gaping between them — cosmic voids. This structure is called the cosmic web.

On a steep mountain slope, a single falling rock sometimes triggers an avalanche, and sometimes gets stuck. It all depends on the state of the slope.

In the quiet of the quantum world, there is no emptiness. Particles are intertwined by invisible threads — entanglement. The authors of the work proposed that the very fabric of spacetime is woven from these threads. This is not just a metaphor: they built a mathematical framework where the distance between points is determined by how much shared information they hold.

An ordinary flashlight emits light whose waves oscillate in all directions at once. But pass that light through a special filter, and you get a beam that oscillates strictly in one plane: that's polarized light. When such a beam travels through biological tissue, the tissue's internal structure slightly alters the orientation of the oscillations.

After the Big Bang, according to inflationary cosmology, the Universe underwent rapid expansion and a series of phase transitions.

In the world of two-dimensional materials, states sometimes emerge that are as extraordinary as they are fragile. One of them — the fractional anomalous Hall crystal (FAHC)—is like a quantum centaur: half ordered lattice, half topological liquid.

The crumpled DNA thread in the cell nucleus is not a chaotic knot, but an intricate melody played on a polymer string. Modern experiments Hi-C, like highly sensitive microphones, capture the echo of contacts between distant genome regions, turning spatial organization into a two-dimensional probability matrix.

A handful of matches falls on the table. Each lies however it lands, but in our minds we turn each into an arrow — from one end to the other. Now ask: can you get from one point to another by moving only in the direction of the arrows? A group of points where you can reach any one from any other is called a strongly connected cluster.

Tile a floor with identical triangles, and you get a boring repeating pattern. But what if you want the pattern to never repeat, yet use just one tile? For a long time, mathematicians were sure it couldn't be done: you'd need at least two different shapes. The famous Penrose mosaic is a case in point: rhombi with acute and obtuse angles arrange into an infinitely varied but strictly ordered pattern.

A thin crack runs through glass. At first glance, the fracture line simply reflects the material's brittleness. But if you zoom in to the atomic level, the picture gets more complex: glass starts to resist differently when the crack accelerates.

Imagine a city where streets are not straight but winding, with dead ends and hidden passages. A bike courier will take much longer to deliver a package than in a city with a regular grid of roads. Similarly, molecules inside living tissue: their path depends on how "tangled" the tissue structure is. Scientists built a model that describes the movement of molecules in such a "tangled" environment.

A landscape cut by roads or rivers into isolated patches resembles a shared apartment after partitions are installed: residents no longer bump into each other in the common hallway. Species that once competed for the same food or space now live apart. Competition weakens, and those that would have lost to pushier neighbors in a continuous landscape now survive.

Ring-shaped reefs, atolls, are usually explained like this: corals grow along the edge of a volcanic island while the island slowly sinks. What's left is a hollow ring that can stretch for kilometers. But satellite images show similar rings around very small reefs where there are no volcanoes and no subsidence.

If you spill a handful of colorful beads on the floor, they will land differently: some will clump together, others will scatter into corners. Roughly the same way, galaxies of different colors (blue, green, and red) are scattered across the universe. Scientists decided to measure how 'clumpy' their distribution is using a number called the fractal dimension.

Imagine a city map where streets are replaced by car speeds and buildings by the metal content of stars. Such a map can tell you where the center is and where the outskirts are, even without knowing exact distances. This is precisely the approach astronomers took with our Galaxy, using longitude–velocity (ℓ–v) diagrams.

In the dark clouds of interstellar gas where stars are born, matter gathers into dense knots — future cradles of stars. Astronomers measure distances between these knots from sky photographs, but a photograph is flat while the cloud is volumetric. Converting from plane to volume is not as simple as it seems.

Graphs are considered identical if their 'terrain' matches. Imagine two maps with mountains and valleys: even if drawn differently, the heights and steepness of slopes can be the same.