Catching a Point within a Teragon
This Demonstration presents a solution to the problem of determining if a chosen point of a two-dimensional plane, selected using the locator, is within the region bounded by a regular convex polygon whose edges are replaced with randomized Koch curves. This region is a self-similar fractal curve called a teragon . The internal and external areas exchange colors as the point crosses the boundary.
The region containing the given point is "color 1", while the remaining area is "color 2". Both colors can be customized.
Snapshot 1: the point is inside the teragon
Snapshot 2: the point is outside the teragon
The given point represents the position of the atomic site in a two-dimensional crystal lattice. The teragon represents the boundary of a nanostructure referred to as a quantum dot. Thus, the teragon can be used as a mask that, when overlaid with the two-dimensional lattice, isolates a set of atomic sites forming a quantum dot with rough edges.
This approach has been used to model and study the edge roughness in phosphorene quantum dots . It can also be readily applied to silicene quantum dots  or generalized to study edge disorder in other nanostructures, such as zigzag-shaped graphene nanoribbons [4–6].
 B. B. Mandelbrot, The Fractal Geometry of Nature, New York: W. H. Freeman, 1983.
 V. A. Saroka, I. Lukyanchuk, M. E. Portnoi and H. Abdelsalam, "Electro-optical Properties of Phosphorene Quantum Dots," Physical Review B, 96(8), 2017 085436. doi:10.1103/PhysRevB.96.085436.
 H. Abdelsalam, M. H. Talaat, I. Lukyanchuk, M. E. Portnoi and V. A. Saroka, "Electro-absorption of Silicene and Bilayer Graphene Quantum Dots," Journal of Applied Physics, 120(1), 2016 014304. doi:10.1063/1.4955222.
 V. A. Saroka and K. G. Batrakov, "Zigzag-Shaped Superlattices on the Basis of Graphene Nanoribbons: Structure and Electronic Properties," Russian Physics Journal, 59(5), 2016 pp. 633–639. doi:10.1007/s11182-016-0816-6.
 V. A. Saroka, K. G. Batrakov, V. A. Demin and L. A. Chernozatonskii, "Band Gaps in Jagged and Straight Graphene Nanoribbons Tunable by an External Electric Field," Journal of Physics: Condensed Matter, 27(14), 2015 145305. doi:10.1088/0953-8984/27/14/145305.
 V. A. Saroka, K. G. Batrakov and L. A. Chernozatonskii, "Edge-Modified Zigzag-Shaped Graphene Nanoribbons: Structure and Electronic Properties," Physics of the Solid State, 56(10), 2014 pp. 2135–2145. doi:10.1134/S106378341410028X.