This tutorial or demo describes the evolution of the simplex method while solving for minimum of a function.

Nelder mead simplex method is an algorithm for finding minimum point for a function, and is based on a convex hull concept. The simplex is a structure of dimensions = dimensions of input parameters+1

Since we are minimzing function of 2 parameters, the resulting figure is a 3 point structure or a triangle.

The initial simplex figure is set to an arbitrary value. After each iteration, function values are calculated at the vertex points of the triangles, and four operations are done in either combinations:
-Reflection
-Expansion
-Contraction
-Shrink

The decision is made by reflecting the worst point and checking how the function value at new point compares to the previous points.

To get an intuition for the method, simply play around by pressing "Start" and "Next Iteration" buttons on sheet2, and everything will be clear.
Note that after each time pressing "Next Iteration", the simplex structure moves towards the function minimum and the size also gets smaller. Finally the method coverges when simplex size gets below tolerance, and this returns the function minima