Electrons are injected at the lower left and ride over a bumpy landscape, with the elevation slowly rising toward the top of the image.

Electrons injected at the top of the image travel over a random landscape again resulting in the branched flow pattern, here rendered in the form of a dendritic mountain.

Electrons launched from the upper right fan out and then form branch, as indirect effects of travelling over bumps.

Electrons launched from the center in all directions fan and then form branches, as indirect effects of travelling over bumps.

Electrons flowing over rough terrain exhibit elaborate folds and caustics (lines where one space ends and another begins) made to appear here as thin sheets of folded translucent kelp, which in fact show the same universal caustic structures.

Electrons injected at the bottom form branches caused by riding over hills and valleys induced by charged atoms which donated the electrons.

Electrons launched from the upper left fan out and then form branches, as indirect effects of travelling over bumps.

Flow pattern for electrons riding over a two dimensional bumpy surface where the electrons were injected from the top in a uniform sheet, all initially heading straight down.

Electrons injected at one point contact, the “sun,” flow in a wire riddled with random imperfections. The quantum aspect of the electrons is shown in color: we follow the wave nature of the electrons by assigning red to the crest of the wave, cyan to a trough, continuously around the color circle.

Electron tracks in a nano device, with electrons launched at various places and followed for a short time. Individual electron tracks are visible, and it can be seen how they gather to make caustics after their launch in a narrow range of angles.

Trichaotic combines three aspects of chaos: wave or quantum chaos fills the sky, rotating rotator chaos fills the landscape, and electron track chaos in a nanowire, complete with color coded to quantum phase, fills the foreground.

Electron flow launched from the upper center in a weakly random potential.

Electron flow launched from the upper center in a weakly random potential, showing quantum phase as color, and the decay of the coherence of the phase to the lower right.

Electron flow in a two dimensional electron gas

Paths of electrons followed for a short time, representing the effect of starting the electrons in a narrow beam at two different places on the random potential landscape on which they live.

Electrons launched from a particular point ride over a bumpy landscape, forming cusps and branches as they move away from launch point.

This image shows two kinds of chaos: a random quantum wave on the surface of a sphere, and chaotic electron paths launched over a range of angles from a particular point.

Electron flow launched from the upper center in a weakly random potential.

Electrons launched from the lower left are color coded according to their current direction

In the lower right, short semiconductor electron tracks are recorded from several different starting points, in a simulation of electrons suffering random weak deflections caused by nearby positively charged "parental" donor atoms. Upper left, quantum wave function "moon".

Electron tracks in a nano device, with electrons launched at various places and followed for a short time. Individual electron tracks are visible, and it can be seen how they gather to make caustics after their launch in a narrow range of angles.

Electrons launched from the center in all directions fan and then form branches, as indirect effects of travelling over bumps.

Electron pathways with quantum phase (in color) traveling over a random landscape of hills and valleys, launched from four corners. In memory of Sol Lewitt.

Electron pathways with quantum phase (in color) traveling over a random landscape of hills and valleys, launched from four corners. In memory of Sol Lewitt.