WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Generalized Ulam Sets in the Plane

​
step size N
25
preset vectors
(1,​φ​)​,​(​φ​,1)
plot transformations
None
random two-vector
random three-vector
This Demonstration plots a list of points of the generalized Ulam set
U
N
in the plane after
N
steps of iteration. The recursive rule to generate
U
N
is to append vectors to the previous set of minimal Euclidean norms that can be uniquely written as the sum of two distinct vectors from
U
N-1
. The specified list of linearly independent initial vectors completely determines the points.
Set the "step size
N
" for the
U
N
plot, keeping in mind that any setting
N≥100
may be slow.
The list of two or more initial vectors may be specified by selecting one of the preset initial vector combinations or randomly.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.