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 {::IMeNZhn2t35SPutNQc87Lw+dQQnaBasFpenCeJLaDQgdQA20cooAG0y02qRWSQS2b8+pvk69  r120dT6mmJHCWTy/zMa4IKR+LZ96EqXGN413ejiSmfWAjo+JaALMzPkp8JaiPNzPKMVV5B/V  ZbJOaIltM/NbzIm6GKB0jskUilQtXCblfWKR9d+7UeTwe2vqPFZMFrhRqKUuBpB+0U/wNkjs  0bvJXaub9oxCfQUPgI4fR5AW83ZJ0wU/825yjipe+ZHJINNldskNsdRrYkARcwCF2YHLbb0K  yu9BZ+x000C9x0E+VSh/2Rjj5Ovwj8WZJEtJopc7R3ESmYYyjxN8LfXtCtrjS2lSQ3eT9nyl  u2nnco74pp7zohroJrms/LrVV4WM5IR9tsQWiv3Hr0oK0Evo2G3FwDOi6fHscy+glv+dzezi  5RHY3lHQjO4JHWspwo5X9j0ddDiB8EmYfKL58jbbUi/ji0iV+fGxQcrw7Hbe7NiG3HQzTK7o  fxXkQR62OKxsEvtMvPTiWvuV6K/SedRCpMZd/D+ZebvLa3yofvwaqcXeYxw2bi4S3OSeslK1  hjdQasXnrPlj49n6vLOglm7DCeoFiXEH9APFgn+E6zV6JiuxlvjXNdsoUVZYvpZURmf6ICTZ  sVkXh4TKj661LuvMJi6mvefU2W+NEV9qeatdzfndsV/s4a9sDuMSe8+TObPJERQDv89XS9DI  hRjm28X+xjx8iv/UZl/Bx6GpqjMoy+EudUHXMkMhl4r7MSvFrcYYOuWvowS7/bvy6kJDc3Zo  PuNhxmxOwCusJJsETSYZmkEDeYwIWc8kiiXMPPpNeRd3RmXFjmeu4IfdfP6y0TGs8njcurH+  DZOV/n/iLflxzOqmf+P6tqP/2dWwykosiB8XCDVsA4lYMpmp7qTiZ9uC7HySbiq6hRvZ9pFV  sA3Ezpy5r0sVy6pilwlzR0Loqt94XK54jXQX4RD8I6SLLKgn3MkU2W/VXydsN/88nzC75XZh  98rtwe+/+C75SsQXXVX8juHIkXbLrzO17n8Uqkr4eukF3zbKulXmo4WTSVSXbPrbt9M6ulro  X6DjbZmrsqe21WVLE2NY5yRSI/KWqe2l/U8eiksYWoZJNlReMfDZXmk1E+WPlyFXRl5sqbzQ  SKb515GpVJ/tNzqut5sVCnac8JsL4FxrfPcmxo2o+lwphJD79kvEev3B3PMlHrFH6R+Oc55y  woQ2t3EtPbYXBRbGdj/eB934/bTor85NdXUAfv0hbKXjwr8jlbbtxC8FWq+wi73Fx3I0YKGs  51+9W95mVXGovMwaPyBDr3jI62pYfW8sDBhdmwHQlBzzUp5hOPFqwfIa+JGRcdV85PW9LEDu  jytERrqFMusFklttuDK3fl9ZYU2njljmhrVd729tipW9ItsQWtNidLHY6aYbU1hrZjGTLDn6  2rtejV4XBd9ISrlH1RGVWFhNa5ObDbnGjgMsGXjxArbWF0W6WuGIcLjYXF2ID+ljDysqDXju  aqbfkrHcd4rjsQ26VDG3Mdg4pEbL7qOMyvPsRDGrV3V/pDsZj1ttdsqb3G3YEEyG7YpXVagr  DfhGN36Iytv11LqrrHsrZd9lerw3WXzxtKFrbY0VQTqQfQ4rXH+m686Tzq6O96SpWZS964uW  e7Ee5pV27OjiBqVfWmYTzaxj0oluQ+w25OaYjiKwRa10ujNMsqrnGzji6jRaF7MegorbOWrG  6j1aRRQrOO9BAjm4abCHC8X7DB+pPBYzxNBc8vwx/CH/Lc8v/P44fzfEDcEwwRADHB8z9RA/  hogjvn9QWU43NHBc/Q+qPCYJK3m3su3rqfjrL+wcDOuI3hfQUwKl2VsN81yJ6ydgraSfar83  4QaJY5loL/hHbIvXMlXil8SslXij8ScvipS5n+/MfrfE1U/wf6xfW9KIVg+qSqoI+wFnhscR  Gm48VGKiY3UF3dXsmkczVBxblNbkmxilOKvsjFGgpAwUAYK9gpcJbJCopA0UAaKANFgmCQT5  5mmimolOEVK4n0DqCQU5Z9fW9O65/B4qAcVAuKAXFgryJ5qIsDgWBQrAoVA0KAaFAtCgWBQr  8DFaF4/oKAbFgtCwWBYrAsVA2KAbFgtyLL2KT0wmAflvj4rYD8VA+KAfFgvy/d8VOX8W+YFA  zCgZBwsAYWAMLAmFAzCgZBwsAYWAMLAmFAzCgZBwsAYWAMLAmlf4wsgBELvg/lCGAXBgrAwV  A4Kv8hrcuvXIOjZoDr4AqKAVFgqCQVBoqAUVAqKAVFgqCQVBoqAUVAqKAVFgqCQVBoqAUVeJ  +LGszRUB+aW5b2312n6rbbAtCgWBQrAoVgvut1AuKAXFgrCwVB4qAcVAuKAXFgrCwVB4qAcV  AuKAXFgrCwVB4qAcV+2wV5fAmwXeiB==}`

I&rsquo;ve uploaded a new version of jlb.ulb with a new fractal plug-in formula, ThreeLevel. It&rsquo;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&rsquo;s zero, then the transition between formulas is abrupt, as in most Barnsley-type formulas. If it&rsquo;s above zero, there&rsquo;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&rsquo;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. ![604e375b8852a.jpg](serve/attachment&amp;path=604e375b8852a.jpg) ValentineVariations { ::IMeNZhn2t35SPutNQc87Lw+dQQnaBasFpenCeJLaDQgdQA20cooAG0y02qRWSQS2b8+pvk69 r120dT6mmJHCWTy/zMa4IKR+LZ96EqXGN413ejiSmfWAjo+JaALMzPkp8JaiPNzPKMVV5B/V ZbJOaIltM/NbzIm6GKB0jskUilQtXCblfWKR9d+7UeTwe2vqPFZMFrhRqKUuBpB+0U/wNkjs 0bvJXaub9oxCfQUPgI4fR5AW83ZJ0wU/825yjipe+ZHJINNldskNsdRrYkARcwCF2YHLbb0K yu9BZ+x000C9x0E+VSh/2Rjj5Ovwj8WZJEtJopc7R3ESmYYyjxN8LfXtCtrjS2lSQ3eT9nyl u2nnco74pp7zohroJrms/LrVV4WM5IR9tsQWiv3Hr0oK0Evo2G3FwDOi6fHscy+glv+dzezi 5RHY3lHQjO4JHWspwo5X9j0ddDiB8EmYfKL58jbbUi/ji0iV+fGxQcrw7Hbe7NiG3HQzTK7o fxXkQR62OKxsEvtMvPTiWvuV6K/SedRCpMZd/D+ZebvLa3yofvwaqcXeYxw2bi4S3OSeslK1 hjdQasXnrPlj49n6vLOglm7DCeoFiXEH9APFgn+E6zV6JiuxlvjXNdsoUVZYvpZURmf6ICTZ sVkXh4TKj661LuvMJi6mvefU2W+NEV9qeatdzfndsV/s4a9sDuMSe8+TObPJERQDv89XS9DI hRjm28X+xjx8iv/UZl/Bx6GpqjMoy+EudUHXMkMhl4r7MSvFrcYYOuWvowS7/bvy6kJDc3Zo PuNhxmxOwCusJJsETSYZmkEDeYwIWc8kiiXMPPpNeRd3RmXFjmeu4IfdfP6y0TGs8njcurH+ DZOV/n/iLflxzOqmf+P6tqP/2dWwykosiB8XCDVsA4lYMpmp7qTiZ9uC7HySbiq6hRvZ9pFV sA3Ezpy5r0sVy6pilwlzR0Loqt94XK54jXQX4RD8I6SLLKgn3MkU2W/VXydsN/88nzC75XZh 98rtwe+/+C75SsQXXVX8juHIkXbLrzO17n8Uqkr4eukF3zbKulXmo4WTSVSXbPrbt9M6ulro X6DjbZmrsqe21WVLE2NY5yRSI/KWqe2l/U8eiksYWoZJNlReMfDZXmk1E+WPlyFXRl5sqbzQ SKb515GpVJ/tNzqut5sVCnac8JsL4FxrfPcmxo2o+lwphJD79kvEev3B3PMlHrFH6R+Oc55y woQ2t3EtPbYXBRbGdj/eB934/bTor85NdXUAfv0hbKXjwr8jlbbtxC8FWq+wi73Fx3I0YKGs 51+9W95mVXGovMwaPyBDr3jI62pYfW8sDBhdmwHQlBzzUp5hOPFqwfIa+JGRcdV85PW9LEDu jytERrqFMusFklttuDK3fl9ZYU2njljmhrVd729tipW9ItsQWtNidLHY6aYbU1hrZjGTLDn6 2rtejV4XBd9ISrlH1RGVWFhNa5ObDbnGjgMsGXjxArbWF0W6WuGIcLjYXF2ID+ljDysqDXju aqbfkrHcd4rjsQ26VDG3Mdg4pEbL7qOMyvPsRDGrV3V/pDsZj1ttdsqb3G3YEEyG7YpXVagr DfhGN36Iytv11LqrrHsrZd9lerw3WXzxtKFrbY0VQTqQfQ4rXH+m686Tzq6O96SpWZS964uW e7Ee5pV27OjiBqVfWmYTzaxj0oluQ+w25OaYjiKwRa10ujNMsqrnGzji6jRaF7MegorbOWrG 6j1aRRQrOO9BAjm4abCHC8X7DB+pPBYzxNBc8vwx/CH/Lc8v/P44fzfEDcEwwRADHB8z9RA/ hogjvn9QWU43NHBc/Q+qPCYJK3m3su3rqfjrL+wcDOuI3hfQUwKl2VsN81yJ6ydgraSfar83 4QaJY5loL/hHbIvXMlXil8SslXij8ScvipS5n+/MfrfE1U/wf6xfW9KIVg+qSqoI+wFnhscR Gm48VGKiY3UF3dXsmkczVBxblNbkmxilOKvsjFGgpAwUAYK9gpcJbJCopA0UAaKANFgmCQT5 5mmimolOEVK4n0DqCQU5Z9fW9O65/B4qAcVAuKAXFgryJ5qIsDgWBQrAoVA0KAaFAtCgWBQr 8DFaF4/oKAbFgtCwWBYrAsVA2KAbFgtyLL2KT0wmAflvj4rYD8VA+KAfFgvy/d8VOX8W+YFA zCgZBwsAYWAMLAmFAzCgZBwsAYWAMLAmFAzCgZBwsAYWAMLAmlf4wsgBELvg/lCGAXBgrAwV A4Kv8hrcuvXIOjZoDr4AqKAVFgqCQVBoqAUVAqKAVFgqCQVBoqAUVAqKAVFgqCQVBoqAUVeJ +LGszRUB+aW5b2312n6rbbAtCgWBQrAoVgvut1AuKAXFgrCwVB4qAcVAuKAXFgrCwVB4qAcV AuKAXFgrCwVB4qAcV+2wV5fAmwXeiB== }

0

Thanks for sharing your formula. Looks interesting!

Thanks for sharing your formula. Looks interesting!

Chris Martin
Gallery: Velvet--Glove.deviantart.com

Currently using UF6.05 on Windows 11 Professional 64-bit

0

I developed the SFormulas so that I could mix M-type and J-type, and combine basic formulas to make my own complicated formulas. I'd like it if some other people tried them out.

I developed the SFormulas so that I could mix M-type and J-type, and combine basic formulas to make my own complicated formulas. I&#039;d like it if some other people tried them out.

0

ThreeLevel does seem quite complicated... to my simple mind anyway.

As formulas and maths goes over my head I usually work visually and with a lot of trial and error. So do bear that in mind when looking at my first attempt here, a heavy adaptation of one of your layers:

``````Waterfall {
; Copyright © 2021 by Christine-Ann Martin.
::GUwq7hn2diVbPOqNQ4vvS7/BEftaJYbw2cV8h2VtnUVS1JtXVlqqUkDY2474tCe39y+rvDvG
IwmEy3gZmnnZ8MD2jJqQEoFxf6+7MM0Kds038vFaZRkIO204NVoevPyGZbsXqeevu55YxBZR
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oy+YcLoFYMwTi2FivrzY2vb/YQX9edTAqDb9V01BJyXoFp7XkTaOBw2COYl7QZrewG6G4I7L
2AOkGxV8RwI7xLEwuFaf+29qwFVp2MuveDcymMeXRmuxg/tiomz6vGyuxm7N3azdFwTD5FTx
1vz3YU3UD+m2G8l6szNxyHhaZtnbWY3WVUJ2GIiDuBYZxhVTItIU1t2LJvtecv9aRyuQxy3y
e9N2Vv+W7qrAOOYB4oFA/G2xed/x6W2MPuLBa1ss5IXKdZeepN3VY2JKl+vf174vG2xvUluI
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5k6yGxhT3qAqIzYe1v1aGpY+8BCh4OnUHycSZ4TI5+7+fsdh00L=
}
``````
ThreeLevel does seem quite complicated... to my simple mind anyway. As formulas and maths goes over my head I usually work visually and with a lot of trial and error. So do bear that in mind when looking at my first attempt here, a heavy adaptation of one of your layers: (wasntme) ![605111e9e2398.jpg](serve/attachment&amp;path=605111e9e2398.jpg) ```` Waterfall { ; Copyright &copy; 2021 by Christine-Ann Martin. ::GUwq7hn2diVbPOqNQ4vvS7/BEftaJYbw2cV8h2VtnUVS1JtXVlqqUkDY2474tCe39y+rvDvG IwmEy3gZmnnZ8MD2jJqQEoFxf6+7MM0Kds038vFaZRkIO204NVoevPyGZbsXqeevu55YxBZR pPqCUQhMUpL9NfcfhqUrSlP8LppGbEFwz/MZFiuCbjRm3fXNqaHFIy1qsUfz1ViMImGZ5iAl +AQvtRiUvPL0P5lYtKXUWaoLEpl5iCZq2/gs8+7SE55q0nb4CkKL8ttQEEFTcJcOzdltF2Gh QUCCCYsRi45UfE2yl44ypGi0nhFKCzsQucYVElVAeTUzXi4HqKCROImRusIYvM47+ZRRGiwv 9SZdEYEpilpiEIZ9t4dWvElYWBFikiD+mP9mSHs/xskdZ/eDxmG5bfd7U5VL3Kg5bbjgHjh1 bLpx7+0fs+XHiycqtWvu9ZZqsQFUn6moM6cOC0XqSyjll1+wHPlh8t5ZvBZD8qPAfNygqobe 4Ji0wDNVNjpaL1Qbiv9qZAWKlh+Pgswuz66otP1mERjzX/ZmeP0b0p188YHn/uotdPXtWvox tRy7Pd2qtVKyHNd5r2JUx+pZzm2U7+6hco57fMCVvKLeWWaOjRt6qc7sOuxEdFTJZhzot5zk HccnHcQWarD+tHonNbgHXi+6+Cpct8VZ81VlwLoKhXSVqy4pBTz+anBU+2N1Zt57qHbZdbMa 1liDoAA1z3NCz0/kRwFTHQLjFjdJrw+YLE9cmc51a9evg3svQFewz/14q9Xkigsgvftl6B8s oy+YcLoFYMwTi2FivrzY2vb/YQX9edTAqDb9V01BJyXoFp7XkTaOBw2COYl7QZrewG6G4I7L 2AOkGxV8RwI7xLEwuFaf+29qwFVp2MuveDcymMeXRmuxg/tiomz6vGyuxm7N3azdFwTD5FTx 1vz3YU3UD+m2G8l6szNxyHhaZtnbWY3WVUJ2GIiDuBYZxhVTItIU1t2LJvtecv9aRyuQxy3y e9N2Vv+W7qrAOOYB4oFA/G2xed/x6W2MPuLBa1ss5IXKdZeepN3VY2JKl+vf174vG2xvUluI XcDdqr7+sDtQY7uN3sYUL/zo1X9JEnzOog1Nqe34yzNr+lHV/sTq3Mo+HMn+JjprSLhot5++ Vz2FBZz0sU593l9ieqqy/rQbUIzlCNY2gL++EMHRooI06lg4h3+9zNf+/5CRoCE9YWcWBcLo 29QCaft9iuHJB24p7ltPlkBXdaOETuu7pa7e/4uPTw3GYDtciZncEyYlV3MDyV+IM3CMojw6 8WZdoXlpgDZF1/kDC1QBH7+DfHbPjam8RUmrnDzpTBBX/nMq1xpUXqDvXlTrc7WJAdnIgNCM B50xLFNwfMHWHpcyYzrw3q5Uy5dhMlQ9cQ4WxI4pWqdgVCs33ROQE08YmsUQEWrECiiYNZhW Vu95KEkNYUWnCOaAGMunLeP7DYhf0BMGn2ZM+YlAxwcKxrTBBdMZWhx2D3r60wHPI8Zeue9k 46dkEwBEbuXXJBPI8HhhPhd+g6qLxBjd7akI9hPHSNEWXuhg7kjh+GiH5YmgMtPiMobkxwI3 OFuDVQgB9HQTf4zpcbHv+IaS4T6T9QTGFRBSa/Hfn8dSj529/BQsbfg4NjQa9iaqcP2MCRYn 5k6yGxhT3qAqIzYe1v1aGpY+8BCh4OnUHycSZ4TI5+7+fsdh00L= } ````

Chris Martin
Gallery: Velvet--Glove.deviantart.com

Currently using UF6.05 on Windows 11 Professional 64-bit

0

True, it is somewhat complicated, though simple in concept (3 formulas: upper, middle, and lower). Many formulas in the database are complicated, such as Strange Brew in tma.ufm, with many parameters to choose from.

Here's another sample.

alt="60561bb5b3b06.jpg">
ThreeLevelExample {
; Copyright © 2021 by Christine-Ann Martin.
::XE1qWhn2trRXvNOOu3Hg5/gRedQ7YJ5P3F+hd7tziZR6eP05e5wBE4Yrk4dcs9Yr2mUs/4Pq
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6Pmt4uHrYF7upd/62PJF8CvuVPs6c88ZGnxuVKN4maYmoEa96f43W+zuct4cav+hVbpN0+qC
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W16vcsDC++nelVPwXYMsYCiU9xH2JHYJJMukgFWT0rcByVBhTzcRbjaA+lrieWrBesLymx51
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