# Buzz Example Gallery

## Calculation of a Distance Gradient

The aim of this code is to have a group of robots form a distance gradient from a source.

There is one robot that acts as the source; for simplicity here it is the robot with id 0. Every robot, including the source, emits its estimated distance from the source, a listens to other robots. * The robots that can see the source directly emit the distance they sense; * The robots that cannot see the source are in two categories:

- Those who don't know any distance yet: these robots emit nil
- Those who received a distance broadcast from one or more neighbors: these robots calculate their distance as the minimum among the received distances

This algorithm keeps running in the `step()`

function, so it can adjust the distance gradient if the robots move around.

- gradient.bzz
function init() { if(id == 0) { # Source robot mydist = 0. } else { # Other robots mydist = 1000. # Listen to other robots' distances neighbors.listen("dist_to_source", function(value_id, value, robot_id) { mydist = math.min( mydist, neighbors.get(robot_id).distance + value) }) } } function step() { neighbors.broadcast("dist_to_source", mydist) } function destroy() { }

## Hexagonal Pattern Formation

Hexagonal patterns can be formed in a simple way by mimicking particle interaction. A simple model of particle interaction is the Lennard-Jones potential, which we use in the following code in a slightly modified way. Instead of the big exponents (12 and 6), we use the exponents 4 and 2, which give us smaller but more manageable numbers.

The idea in the code is that every robot can use the `neighbors`

structure to sense the distance and angle of every direct neighbor. Using the distance, we calculate the magnitude of the “virtual force” (attraction or repulsion) due to a neighbor (function `lj()`

). We then use the force magnitude and the angle to make an interaction vector (function `to_lj`

), and proceed to sum all of these contributions together into an accumulator vector (functions `sum`

and `neighbors.reduce()`

). Finally, we scale the accumulator and feed it to the `goto()`

function, which transforms a 2D vector into motion.

- hexagon.bzz
# We need this for 2D vectors # Make sure you pass the correct include path to "bzzc -I <path1:path2> ..." include "include/vec2.bzz" # Lennard-Jones parameters TARGET = 283.0 EPSILON = 150.0 # Lennard-Jones interaction magnitude function lj_magnitude(dist, target, epsilon) { return -(epsilon / dist) * ((target / dist)^4 - (target / dist)^2) } # Neighbor data to LJ interaction vector function lj_vector(rid, data) { return math.vec2.newp(lj_magnitude(data.distance, TARGET, EPSILON), data.azimuth) } # Accumulator of neighbor LJ interactions function lj_sum(rid, data, accum) { return math.vec2.add(data, accum) } # Calculates and actuates the flocking interaction function hexagon() { # Calculate accumulator var accum = neighbors.map(lj_vector).reduce(lj_sum, math.vec2.new(0.0, 0.0)) if(neighbors.count() > 0) math.vec2.scale(accum, 1.0 / neighbors.count()) # Move according to vector goto(accum.x, accum.y) } # Executed at init time function init() { } # Executed every time step function step() { hexagon() } # Execute at exit function destroy() { }

## Square Pattern Formation

To form square lattice, we can build upon the previous example. The insight is to notice that, in a square lattice, we can color the nodes forming the lattice with two shades, e.g., red and blue, and then mimic the crystal structure of kitchen salt. In this structure, if two nodes have different colors, they stay at a distance *D*; if they have the same color, they stay at a distance *D* * sqrt(2).

With this idea in mind, the following script divides the robots in two swarms: those with an even id and those with an odd id. Then, using `neighbors.kin()`

and `neighbors.nonkin()`

, the robots can distinguish which distance to pick and calculate the correct interaction vector.

- square.bzz
# We need this for 2D vectors # Make sure you pass the correct include path to "bzzc -I <path1:path2> ..." include "include/vec2.bzz" # Lennard-Jones parameters TARGET_KIN = 283.0 EPSILON_KIN = 150.0 TARGET_NONKIN = 200.0 EPSILON_NONKIN = 100.0 # Lennard-Jones interaction magnitude function lj_magnitude(dist, target, epsilon) { return -(epsilon / dist) * ((target / dist)^4 - (target / dist)^2) } # Neighbor data to LJ interaction vector function lj_vector_kin(rid, data) { return math.vec2.newp(lj_magnitude(data.distance, TARGET_KIN, EPSILON_KIN), data.azimuth) } # Neighbor data to LJ interaction vector function lj_vector_nonkin(rid, data) { return math.vec2.newp(lj_magnitude(data.distance, TARGET_NONKIN, EPSILON_NONKIN), data.azimuth) } # Accumulator of neighbor LJ interactions function lj_sum(rid, data, accum) { return math.vec2.add(data, accum) } # Calculates and actuates the flocking interaction function square() { # Calculate accumulator var accum = neighbors.kin().map(lj_vector_kin).reduce(lj_sum, math.vec2.new(0.0, 0.0)) accum = neighbors.nonkin().map(lj_vector_nonkin).reduce(lj_sum, accum) if(neighbors.count() > 0) math.vec2.scale(accum, 1.0 / neighbors.count()) # Move according to vector goto(accum.x, accum.y) } # Executed at init time function init() { # Divide the swarm in two sub-swarms s1 = swarm.create(1) s1.select(id % 2 == 0) s2 = s1.others(2) } # Executed every time step function step() { s1.exec(square) s2.exec(square) } # Execute at exit function destroy() { }