Celluar Automata-Based Evolving Self-Controlled Light Pattern Generation on LED Canvas

Charles Kim

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In every side of us, optical technology and lighting industry are increasingly revolving around light emitting diodes (LEDs) replacing the traditional light bulbs in general lighting, energy-saving applications, and architectural and entertainment sectors.  The wide-spread use of LEDs in beautifying buildings and streets and parks and skylines has fascinated people around the globe.

The focus of this LED application is about drawing evolving patterns in each discrete time step with lights on a canvas of LEDs.  The drawing mechanism is not done by the conventional light control method, which, using a central computer with control wires connecting each of the lamps in an array of lamps, controls each every lamp to produce a desired pattern in the array.   Instead, the drawing on the canvas is, ironically, a by-product of the collective, synchronous action of each individual LED which does nothing but select its color, determined using a very simple rule, for the next discrete time step, by the present states of its neighboring LEDs.  In analogy, the resulting pattern on the LED canvas resembles the global manifestation of all local activities whose governing rules are the same, or a complex system built from simple components.  This autonomous, self-control of each LED by its neighboring conditions in an LED array is based on a mathematical algorithm called cellular automata, a discrete mathematical modeling basis.

Cellular automata are an alternative, complementary basis for mathematical models of system to differential equations which are generally suitable for systems with a small number of continuous degrees of freedom, evolving in a continuous manner.   Cellular automata describe the behaviors of systems with large numbers of discrete degrees of freedom.  Put another way, cellular automata represent a mathematical idealization of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values.

More specifically, cellular automata consist of a discrete lattice ("array") of sites ("cells"). Each site takes in a finite set of possible values and the value of each site evolves, in discrete time steps, simultaneously, according to the same deterministic rules. The rules for the evolution of a site depend only on a local neighborhood of sites around it.  Because of these advantages, cellular automata have been applied in biological systems to model growth of organisms or populations of plant with local ecological interaction.

The idea of self-change of LED color by the states (i.e., colors) of its neighbors eliminates the need of a central processor and control wires from the central processor to each of the LEDs in the array.  To be used in the light canvas and thus utilized in the cellular automata scheme of color change, traditional LED fixture should be additionally equipped with a low-end microprocessor, as illustrated in the Figures 1 and 2, to execute a cellular automat rule for determining its color state for the next time step, and a number of color sensors to read the current time color states of the neighboring LEDs.

Optionally, instead of installing color sensors, a processor with wireless (WiFi or Bluetooth) or power line carrier connectivity would be equipped so that it receives the color states from the microprocessors in the neighboring LEDs (see Figure 3).    This color reading is in all LEDs in the array at the same time, and the execution of the rule, same for all the LEDs, is performed simultaneously at the subsequent time.

One example of a rule, in an array of 8-neighbor configuration illustrated in Figure 4, simultaneously applying to each of the LEDs, is “If 2 neighbors out of 8 are in RED color in the current time step, then the color of the self in the next time step is RED."   Another example of a rule is: "If the left neighbor LED's color is RED and the right neighbor LED's status is BLUE in the current time step, and the current color of self is RED, then the self’s color in the next time step is GREEN."  An example light pattern simulated using a simple rule is depicted in Figure 5.

The effect of the same rule for all LEDs, seemingly simple and dull, can generate in the array level very beautiful natural light patterns on the light canvas.   A future plan of expanding this LED canvas idea is to make a cube (see Figure 6), with a light canvas on all sides except the bottom which will house a stand and base to hold the cube.  Each side will be run on the selected rules of cellular automata, and the patterns corresponding to the rules on its respective light canvas will be generated independently.  Therefore, the beautiful light patterns of the cube can be observed and appreciated at all sides and above.  Moreover, I plan to install a Bluetooth-  and Power Line Carrier-capable controller with a display at each side so that it can, first, receive observers’ rule numbers sent from their smartphones and, second, it send the rules to the each of the LED modules on the light canvas.  By this interaction of observers and the LED canvas cube, it can provide more engaging experience with lighting technology, smartphones, and lighting with LEDs.