MatedJulias { ; ; This formula was first implemented in C++ by Thomas Ludwig (lycium), then ; adapted to Ultra Fractal and expanded on by Jess Darling (FarDareisMai). ; init: z = #pixel loop: znum = (z ^ @expnum) + @seed zden = (z ^ @expden) - @c1 m = znum / zden n = @seed2 + (@c2 / ((z ^ @coarse) - (@seed2 ^ @fine))) z = (m / n) * z bailout: |z| <= @bailout default: title = "Mated Julias" param seed caption = "seed" default = (0.45,0.7794228634) hint = "Use this parameter to create many different Julia sets. A good \ way to set this parameter is with the Eyedropper, or Explore\ features." endparam param seed2 caption = "secondary seed" default = (0.9,0.2931446) hint = "This parameter is very sensitive to small changes." endparam param expnum caption = "num exp" default = (2,0) hint = "This parameter sets the exponent for the Julia formula. \ Increasing the real part to 3, 4, and so on, will multiply the \ symmetry of the Julia figure. Non-integer real values and non-zero \ imaginary values will create distorted Julia fractals. Use (2, 0) \ for the standard Julia set." endparam param expden caption = "denom exp" default = (2,0) hint = "This parameter sets the exponent for the Julia formula. \ Increasing the real part to 3, 4, and so on, will multiply the \ symmetry of the Julia figure. Non-integer real values and non-zero \ imaginary values will create distorted Julia fractals. Use (2, 0) \ for the standard Julia set." endparam param bailout caption = "bailout" default = 1024.0 min = 1.0 hint = "This parameter defines how soon an orbit bails out while \ iterating. Larger values give smoother outlines, but may cause \ the inside portion of the fractal to grow or even fill the whole \ image." endparam param fine caption = "fine mod" default = (2,-0.91667) endparam param coarse caption = "coarse mod" default = (2,0) endparam param c1 caption = "seed mod" default = (1,0) endparam param c2 caption = "pos mod" default = (1,0) endparam } SerendipitousJulia { ; ; The result of a mistake made while working on the Mated Julias formula. ; init: z = #pixel loop: znum = (z ^ z) + @seed zden = (z ^ z) - @c1 m = znum / zden n = @seed2 + (@c2 / ((z ^ z) - (@seed2 ^ @fine))) z = (m / n) * z bailout: |z| <= @bailout default: title = "Serendipitous Julia" param seed caption = "seed" default = (0.45,0.7794228634) endparam param seed2 caption = "secondary seed" default = (0.9,0.2931446) endparam param bailout caption = "bailout" default = 1024.0 min = 1.0 hint = "This parameter defines how soon an orbit bails out while \ iterating. Larger values give smoother outlines, but may cause \ the inside portion of the fractal to grow or even fill the whole \ image." endparam param fine caption = "fine mod" default = (0,0) endparam param c1 caption = "seed mod" default = (1,0) endparam param c2 caption = "pos mod" default = (1,0) endparam }