I’ve uploaded a new version of jlb.ulb with a new fractal plug-in formula, ThreeLevel. It’s a Barnsley-type formulas; these formulas define a critical value, and at each iteration some combination of z and c is compared to the critical value. If the combination is above the critical value, one formula is used; if below, another formula is used.
ThreeLevel uses two critical values and three formulas, upper, middle, and lower. (If the two critical values are equal, the middle formula is not used.) All the formulas have to be SFormulas, defined in jlb.ulb.
There is also a transition parameter. If it’s zero, then the transition between formulas is abrupt, as in most Barnsley-type formulas. If it’s above zero, there’s a smooth transition using all three formulas.
ThreeLevel is an SFormula that plugs into SwitchCombo from jlb.ulb, which plugs into Switch Combo Formula from jlb.ufm. (You can use the example as a template for experimenting.)
The example fractal shows six variations on my Valentine 2021 fractal. Each variation is one layer, and all use the same gradient and the same simple coloring. They are arranged using a new plug-in transformation in jlb.ulb, MoveCenter, which just shifts the layer’s center to another location using screen-relative coordinates.
The upper formula is a Mandelbrot/Julia variant. The middle formula is a convergent Newton/Julia variant. The lower formula is a standard convergent Lambda. The overall effect is divergent.
Starting from the upper left corner and going clockwise (or counter-clockwise!) exactly one of three values, the two critical values and the transition parameter, is slightly changed from one fractal to the next.
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}
I’ve uploaded a new version of jlb.ulb with a new fractal plug-in formula, ThreeLevel. It’s a Barnsley-type formulas; these formulas define a critical value, and at each iteration some combination of z and c is compared to the critical value. If the combination is above the critical value, one formula is used; if below, another formula is used.
ThreeLevel uses two critical values and three formulas, upper, middle, and lower. (If the two critical values are equal, the middle formula is not used.) All the formulas have to be SFormulas, defined in jlb.ulb.
There is also a transition parameter. If it’s zero, then the transition between formulas is abrupt, as in most Barnsley-type formulas. If it’s above zero, there’s a smooth transition using all three formulas.
ThreeLevel is an SFormula that plugs into SwitchCombo from jlb.ulb, which plugs into Switch Combo Formula from jlb.ufm. (You can use the example as a template for experimenting.)
The example fractal shows six variations on my Valentine 2021 fractal. Each variation is one layer, and all use the same gradient and the same simple coloring. They are arranged using a new plug-in transformation in jlb.ulb, MoveCenter, which just shifts the layer’s center to another location using screen-relative coordinates.
The upper formula is a Mandelbrot/Julia variant. The middle formula is a convergent Newton/Julia variant. The lower formula is a standard convergent Lambda. The overall effect is divergent.
Starting from the upper left corner and going clockwise (or counter-clockwise!) exactly one of three values, the two critical values and the transition parameter, is slightly changed from one fractal to the next.
ValentineVariations {
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}
alt="60561bb5b3b06.jpg">