__The Koch Snowflake Spiral__

*On route to understanding if fractals have a 'wavy' like nature, I finally put pencil to paper and drew what I've been thinking.*

*I have been pondering on what effect a 'mutation' or change to one triangle - a dot at the apex of the triangle as shown below - would have or show on the*

*iterating*

*Koch Snowflake. I envisaged that it would spiral to infinity as shown below.*

*By tracing a smooth curve through the (red) 'dots'**series of**iterated mutant triangles, I would develop - what looks like - a kind of logarithmic spiral, or a wave or pulse if this spiral curve was viewed in the front elevation view as opposed to the plan elevation (above).***Method**

As a circles radius (what the compass is set to) scribes 6 times around the circles circumference, the three corners of the 1st equilateral triangle (iteration 1) can be produced, and the apex of the 2nd triangle (iteration 2) can also be marked. With the compass still at this 1st setting, a segment of the Koch Spiral - from apex 1 to apex 2 (iteration 1 to iteration 2) - is created. The apexes of every triangle in the iteration series are the tangent points of the spiral.

Find the centre the 2nd triangle, and repeat the process. The process can be repeated - both zooming in or zooming out - to infinity.