## Galaxy clusters

#### Abell 3376

This is a simulation of a collision of two galaxy clusters. Colors represent the intracluster gas density. Dark matter is present in the calculations, but not displayed in this visualization. For details, see the paper Machado & Lima Neto (2013).

#### Off-axis merger

In this low-resolution illustrative example, two clusters undergo a non-head-on collision.

## Barred galaxies

#### Face-on

This simulation shows the evolution of a barred spiral galaxy. Only stars are shown, and colors represent their density. The dark matter halo is also present in the calculations, but not displayed in this animation.

#### Edge-on (almost)

When the same galaxy is viewed under an inclination angle, one may notice the vertical thickness of the peanut-shaped bulge.

#### Stellar disk and dark matter halo

In this animation we see the evolution of a barred galaxy (in blue), but also of its dark matter halo (in orange). Both are seen face-on and edge-on. As the bar develops, the initially flattened halo becomes more spherical. For details, see the paper Machado & Athanassoula (2010).

#### Slowly rotating

This animation shows the stellar disk of a simulated barred galaxy. Displaying more frequent time steps provides a better glimpse of the orbital structure.

## Gravitational N-body problem

#### Orbits

The orbits of these particles were obtained by direct summation (i.e. explicitly computing the gravitational forces at each successive time step to obtain their positions). This animation illustrates initial conditions resulting in: a circular orbit, elliptical orbits of different ellipticities, a hyperbolic encounter, a three-body problem (including the particular case of a so-called "figure eight choreography"). Finally, the orbits of 1000 particles distributed as a Plummer sphere are shown.

#### Direct summation

This is an illustration of the required number of force computations to solve the gravitational N-body problem numerically by direct summation. For N bodies, N(N-1) computations are needed at each time step.

#### Tree code

This is an approximate illustration of the basic idea behind the tree algorithm, which is often employed to solve the gravitational N-body problem numerically (Barnes & Hut simulation).