In addition to tilings of the plane by rep-tiles these are several other classes of tilings of the plane by the attractors of IFSs.

**1.** Trivially, the plane may be tiled by copies of a rep-n rep-tile
differing in area by *n ^{m}*. This can be
represented as an IFS as follows. Take the IFS for a rep-tile, with transforms

**2.** Trivially, there are classes of rep-tiles that occupy an integral
fraction of another tile, and which can be fitted together to recreate the
original rep-tile. Commonly there is more than one such rep-tile for each
symmetric tile, and hence tilings of the plane are possible in which not all
the copies of the original symmetric rep-tile are dissected in the same way.
Both periodic and non-periodic tilings are possible.

**3.** Trivially, given a IFS for a rep-tile, with transforms
**T _{i}**, a new IFS with transforms

**4.** There are other self-affine IFSs which have attractors which tile
the plane. For example the sunburst, sunrise and starburst triangles are not
self-similar constructions, but tile the plane.

**5.** Given a rep-tile, whose IFS has transforms **T _{i}** we can create a new IFS by dividing the transforms
into disjoint non-empty sets

Documenting these figures is of lower priority, and at the moment only the
*metatrapezia* (derived from the *triamond*) are available on these
web pages.

**6.** Fractals can be constructed as one or many armed spirals

- Koch Snowflake (1 tiling fractal): 6 armed
- Metatrapezoidal Snowflake (1 tiling fractal): 12 armed
- Rauzy Fractal (1 tiling fractal): 2 armed
- minimal Pisot tile (1 tiling fractal): 1 armed
- 2 element ir-rep-tiles (7 tiling fractals,
including the
*minimal Pisot tile*): 1 armed - pseudo-terdragon (1 tiling fractal): 2 armed

Grouped element derivatives of symmetric members of the class can be created

- Koch teardrops (4 tiling fractals): grouped element derivatives of the Koch Snowflake.
- demiRauzy tiles (12 tiling fractals)
- demi-pseudo-terdragons (10 tiling fractals)

as can *metafigures*.

- m-pseudo-terdragons (3 tiling fractals)
- m-demi-pseudo-terdragons (4 tiling fractals)

and grouped element derivatives of metafigures

- demi-m-demi-pseudo-terdragons (10 tiling fractals)

R. William Gosper has published another derivative of the Koch Snowflake

- Gosper's frozen teardrop (1 tiling fractal)

**7.** There are other attractors which tile the plane, but are not
rep-tiles, and which are self-similar with copies of different sizes, which are
to the best of my knowledge not reachable by the algorithm described in
**5**, and which are neither composed of spirally arranged elements, nor
derivable from such fractals.

- mapleleaf tile (3 tiling fractals)
- golden tiles (13 tiling fractals)
- tiles associated with the 3rd unit cubic Pisot number with complex conjugates
- tiles associated with the 4th unit cubic Pisot number with complex conjugates
- a tile associated with the 8th unit cubic Pisot number with complex conjugates, and other tiles with similar contructions.

- sample irreptile from Karl Scherer: tiling of a square by a figure described as an "irregular reptile".

© 2001, 2002, 2005 Stewart R. Hinsley