vertex_colour_from_polygon_size.py

import bpy
from mathutils import Vector

# start in object mode
obj = bpy.data.objects["Plane.001"]
mesh = obj.data

mesh.vertex_colors.new()
color_layer = mesh.vertex_colors.active  
#color_layer = mesh.vertex_colors["Col"]

# first scan through to figure out min and max stretch
verts = mesh.vertices
polys = []
for poly in mesh.polygons:

    face_median = Vector()
    for idx in poly.vertices:
        face_median += verts[idx].co
    face_median *= 1 / poly.loop_total

    qdist = lambda idx: (verts[idx].co - face_median).length
    stretch = sum([qdist(idx) for idx in poly.vertices])
    stretch /= poly.loop_total

    polys.append(stretch)

# now colour them as a function of their relative stretch
min_val = min(polys)
max_dif = max(polys) - min(polys)
i = 0
for g, poly in enumerate(mesh.polygons):
    for idx in poly.loop_indices:
        c = (polys[g] - min_val) / max_dif
        color_layer.data[i].color = (c,c,c)
        i += 1

## set to vertex paint mode to see the result
bpy.ops.object.mode_set(mode='VERTEX_PAINT')