In 1977, Robert Ammann  discovered a set of aperiodic prototiles later called the set A4 by Grünbaum and Shephard . In order to ensure an aperiodic tiling, the original tiling uses either marked tiles or tiles with indentations that must be filled by keys. This Demonstration does not need keys because the substitution rules force aperiodicity. The parameters
can have any positive value (limited to the range
in this Demonstration), but only for
do the Amman bars become straight lines. With increasing iteration levels, the super tiles approach the same shape as obtained directly by setting the parameter ratio to
, that is, when using this ratio, subsequent super tile shapes are similar.
The initial tile (prototile) is shown at iteration level 0; higher levels show iterated super tiles composed of prototiles.
Tiles are colored according to the given level as long as it is at most the current iteration level.
Set the coloring of the involved prototile types.
The bottom slider controls
and the upper slider controls
. Changing the sliders has no visual impact when
is fixed to
Select one of the three involved prototile types as the initial tile.
Use this checkbox to toggle the display of Amman bars; straight lines across the tiling only appear if
Select whether the value of
is forced to
or set by the
slider. The current slider settings are unchanged.
Use this popup menu to select the color of the prototile edges.
 B. Grünbaum and G. C. Shephard, Tilings and Patterns
, New York: W. H. Freeman, 1987 pp. 529–530.