One way to do it with logarithms would be with the function 1 + 1/(log(1-x)-1). This will still map [0,1] to [0,1] monotonically increasing, also with infinite derivative at x=1.
There must be a miskake in this formula, since log(1-x) gives an error for x=1.
The function
x = log(x*4
n+1) / log(4
n+1)
with n = [0...10] (set by a slider control) lets the user determine the degree of the gradient.
Example images:
Original (linear gradient)
n = 0.00
n = 1.00
n = 1.50
n = 2.00
n = 2.50
Using a gamma function instead of a logarithmic one, the gradient becomes a bit softer:
x = x
1/Gamma(Gamma = 0.1...10)
Example images:
Original (linear gradient)
Gamma = 0.50
Gamma = 1.00 (this is equal to a linear gradient)
Gamma = 1.50
Gamma = 2.00
Gamma = 2.50
Sometimes a simple 1/4 sinus curve yields good results:
x = sin(x * Pi / 2)
Example image:
Original (linear gradient)
1/4-Sinus
This function automatically adapts the degree of the gradient to the number of visible iterations/colors:
x = (log(iterations) - log(minIterations)) / (log(maxIterations) - log(g_minIterations))
Example image:
Original (linear gradient)
Auto-Logarithm
The example images were created by this
JavaScript application.
Stefan
March 13, 2012, 05:00:36 PM
Dilber MC Theme by HarzeM