The Hokkaido fractal is a planar self-similar fractal associated with the plastic
constant and the substitution system 
, 
, 
, 
, 
(Jolivet 2013, p. 96). Its name refers to its resemblance
to the Japanese island of Hokkaido (Ei et al. 2006, p. 2288). Let 
be the plastic
constant and let 
be the root of 
with positive imaginary
part, so 
.
A normalization of the fractal is the compact set
 |
(1)
|
Thus successive 1s in the digit strings are separated by at least four 0s (Akiyama and Sadahiro 1998, p. 11).
Grouping these strings according to whether they begin with 0 or 10000 gives the iterated function system
 |
(2)
|
The two pieces have disjoint interiors and area proportions 
and 
, whose sum is 1 (Akiyama and Sadahiro 1998, pp. 13-15).
Thus 
is an irreptile with two pieces of different sizes.
The figure shows a finite approximation with these two
pieces colored separately.
The boundary of 
is a Jordan curve (Luo 2002,
p. 335). Its Hausdorff dimension 
is the positive
solution of
 |
(3)
|
(Akiyama and Sadahiro 1998, pp. 24-26).
