With Ricardo E. Ramirez
Christmas is one of the most popular and enjoyable holidays in Colombia. That is why many classes have fun activities and projects related to this time of the year. This nativity scene was a final project for the Robotics Seminar III of the Master in Industrial Automation.
The user can change the sequence of movement through sensors. The sequence is given by the states of a Cellular Automaton or random boolean network. To find where the sequence converges, we use the software DDLab.
Introduction
One of the most interesting applications of robotics is network structures for large numbers of individuals, colonies, reconfiguration, and biots.
A way to achieve it is through cellular automatons (CA) or random boolean networks (RBN). They allow knowing the evolution through time and the dynamics of the systems. They also allow finding repetitive sequences, called attractors.
Modifying the dependence (wiring) of an individual relative to others, modifies the attractors, period and states in each attractor.
General Considerations
Nativity Scene
The nativity scene has 10 mobile figurines with binary states. The figurine takes the 0 value when it is not moving or the lamp is off, and 1 when it is moving or the lamp is on. The state change is given by the rules of an RBA and depends only of two more nearby values.
Figurines
The figurines and states selected are:
Control Signals
An RBA can be affected by external signals or noise to force change the change of states. In this case we used four external signals.
Design and Assembly
DDLab
DDLab (Discrete Dynamics Lab) is an application developed at the Santa Fe Institute in New Mexico. It allows to visualize the attractors (Basins of Attraction - BOA). We randomly enter the ten nodes of the figurines. Their next state depends on the relationship between two nodes of the previous state. The relationships were randomly picked with a number between 1 and 15.
We used DDLab's mutation utility until it converged to 4 BOAs with 4 or more states in the attractor. Each state is represented by a decimal numeral. After converting this number to binary we have 10 bits, one for each figurine.
The following tables show the states of the basins of attraction and the DDLab chart.
As seen in the tables, the bit number 8 is always on. Because of this we assigned it to the star.
Coding
We developed a program in TurboC. To change the states we used the sensors. If more than one sensor is activated at the time the priority will be decided according to the figure on the left. Thus only one sensor will operate the change of states.
The signals for activation of the figurines are given through the outputs of the computer's parallel port.
The program starts asking the user the wait time between attractors. Then will go to a cycle that will be executed while no computer key is pressed.
Electronics
The communication with an external circuit is achieved through the computer's parallel port.
4 of the port inputs will bring the status of the arrows of a gaming dancing mat (sensors). A change of state happens every time an arrow is pressed.
The outputs of the port are connected to an arrange of opto-triacs with the double function of isolating the port and powering the motors.
Art Design
A watercolor painting made by a local artist is supported on a metallic structure. The moving figurines pop out of the painting. The landscape hides the electronics and moving mechanisms.
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