# Koch Division

Progression of a Koch snowflake as it is described by a recursive definition I wrote in grasshopper

Koch snowflake in Grasshopper

Application of the same principle for a regular tetrahedron made through a recursive hrasshopper definition..

Koch tetrahedron

Paper model for Koch tetrahedron

Paper model

1. Maycon said:

Could you explain the functions (evaluate) you have used?
Thanks!

• korras said:

Yes

A)start from drawing equilateral triangle on XY

B)put the formula of tetrahedron’s height and find the too vertex. Create the geometry to produce the tetrahedron

C)Take the midpoints of the edges of each face and connect them to het a new equilateral triangle

D) then for each face of the tetrahedron, find midpoint. Take the normal vector of its surface at this midpoint and displace the point along this vector the appropriate distance as given by the height formula. Create the new tetrahedron which will be the first iteration of the geometry.

E)make the definition recursive to produce following iterations

All work was done in Grasshoper for Rhino.

Hope that helps!