Attractor of Cantor Type with Positive Measure

We construct an iterated function system consisting of strictly increasing contractions $f,g\text{\hspace{0.17em}⁣}:[0,1]\to [0,1]$ with $f([0,1])\cap g([0,1])=\mathrm{\varnothing }$ and such that its attractor has positive Lebesgue measure.