Previously I’ve looked at fractals created by a point moving half-way towards the random chosen vertex of a polygon. But you can also choose an initial vertex, then choose a new vertex by adding a random number to that initial vertex. Then repeat. For example, if the polygon is a square and the initial vertex is *v* = 1, then choose *v* + 3 = 4 or *v* – 1 = 3, and so on.

You can then ban or un-ban the choice of vertex-jump as you can ban or un-ban direct choices of vertex. These two methods of random choice are effectively the same, but one can be simpler to program than the other. That’s why I’ve come across some new fractals by using vertex-jumps. Here they are:

vertices = 4, vertex-jump = (1,2,3,4), ban on same choice twice in a row

vertices = 4, vertex-jump = (1,2,3,4), ban on 2 in row (black-and-white version)

*v* = 4, *vj* = (1,2,3,4), ban on choice *c* + 2 from previous choice *c*

*v* = 4, *vj* = (1,2,3,4), ban *c* + 2 (animated gif)

*vj* = (1,2,3,4), ban *c* + 2 (black-and-white)

*vj* = (1,2,3,4), ban *c* + 0 at time *t+1* unless *c* + 0 at time *t*-1

*vj* = (1,2,3,4), ban *c* + 0 at *t+1*, unless *c* + 0 at *t*-1 (black-and-white)

*vj* = (1,2,3,4,5), ban *c* + 0

*vj* = (0,1,2,3,4), ban *c* + 0

*vj* = (0,1,2,3,4), ban *c* + 0 (black-and-white)

*vj* = (1,2,3,4), ban *c* + 2 at *t*+1 unless *c* + 2 at *t*-1 (animated gif)

*vj* = (1,2,3,4), ban *c* + various at *t*+1 unless *c* + various at *t*-1 (animated gif)

*vj* = (1,2,3,4,5), ban *c* + 0 at *t*+1 unless *c* + 0 at *t*-1

*vj* = (-2,-1,0,1,2), ban *c* + 0

*vj* = (-2,-1,0,1,2), ban *c* + 0 (black-and-white)

*vj* = (0,1,2,3,4), ban *c* + va unless *c* + va

*v* = 5, *vj* = (1,2,3,4), ban *c* + 0

*v* = 5, *vj* = (1,2,3,4), ban *c* + 2

*v* = 5, *vj* = (0,1,2,3), ban *c* + 3

*v* = 6, *vj* = (0,1,2,3), ban *c* + 2

*v* = 5, *vj* = va, ban *c* + va (animated gif)