Modify triangle spiral
special spiral
This pattern is created by moving the center close to a vertex of the triangle and making the ratio of adjacent sides of that vertex close to the scaling factor.
figure 8
redefine ratio and factor
The same pattern can be created by directly defining the angle and ratio in terms of the measurements of the triangle.
r=distance[B,C]/distance[B,D]
and
t=angle[D,B,C]
In this figure, r and t will be updated when the vertices of the triangle are dragged.
figure 9
applying the same action
The same transformation can be applied to another object (the star shape in the following figure). You can modify the star shape or move it around to see how the same action is applied.