Murthy, V KKrishnamurthy, E.Vikram2015-12-132015-12-131025-5818http://hdl.handle.net/1885/87488A smart system exhibits the four important properties: (i) Interactive, Collective, coordinated and Parallel Operation (ii) Self-organization through emergent properties (iii) Power law scaling under emergence (iv) Adaptive and Flexible operation. We describe the role of fractal and percolation model for understanding smart systems. A hierarchy based on metric entropy is suggested among the computational systems that transcend from the unsmart to the smart system through a phase transition like phenomenon. Understanding smart systems is useful to solve hard-optimization problem inspired by the self-organizing processes found in nature.Keywords: Algorithms; Artificial intelligence; Chaos theory; Computational methods; Digital computers; Entropy; Fractals; Heuristic methods; Mathematical models; Optimization; Phase transitions; Problem solving; Extremal optimization; Fractal dimension; Lyapunov ex Extremal optimization; Fractal dimension; Lyapunov exponent; Metric entropy; Percolation; Phase transition; Smart systems; Time arrow20042015-12-12