self-

theoretical

Dimension

estimated

error (%)

Koch curve

-similary

$\frac{\ln 4}{\ln 3}\approx \text{1}.\text{26185}$

1.26377

0.152

Sierpinski triangle

-similary

$\frac{\ln 3}{\ln 2}\approx \text{1}.\text{58496}$

1.58466

0.019

Sierpinski square

-similary

$\frac{\ln 8}{\ln 3}\approx \text{1}.\text{89279}$

1.88729

0.291

Subsequent triangle

-similary

1.62234

1.62342

0.067

Self-affine square

-affine

1.79649

1.79134

0.287

Barnsley fern

-affine

1.76462

1.76249

0.121

Tree

-affine

1.81616

1.80511

0.612

Sea horse

-affine

1.79616

1.78110

0.846