Solving Systems of Transcendental Equations
Choose an equation or a system of equations from the popup menu. The first three choices are univariate complex analytic equations, the last one is a pair of real equations not derived from a single complex analytic one. You can move around the rectangle in which the solutions are to be found by choosing the coordinates of its center and its width and height. After choosing the equation (or system of equations) to be solved and the region in which to look for solutions, increase the number of iterations to see the rectangles subdivided and tested for the presence of solutions. When there are no more blue rectangles left, all the solutions contained in the region (if any) will be represented by green points.
For the details of Semenov's algorithm see the related Demonstration "Semenov's Algorithm for Solving Nonlinear Equations" and: V. Yu. Semenov, "The Method of Determining All Real Nonmultiple Roots of Systems of Nonlinear Equations," The Journal of Computational Mathematics and Mathematical Physics, 47(9), 2007 p. 1428.