Multifractals

Defining f(α)

For each point (q, τ(q)) say the slope of the tangent line is -α. That is, α = -dτ/dq.

This tangent line passes through the point (q, τ(q)) and the point (0, y). Consequently,

-α = (y - τ(q))/(0 - q)

Solving for y,

y = q⋅α + τ(q)

Call this y-value f(α):

f(α) = q⋅α + τ(q)

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