Mandelbulb 3D Tutorial: Kleinian Spine and Starfish with JosKn-KleinIFS By Persistent Aura (http://persistentaura.deviantart.com/) The JosKn-KleinIFS is a fantastic formula to work with. It is remarkably simple to achieve great results on its own without the need for complicated formula combinations. In this tutorial we will be learning how to create spine- and starfish-like kleinian structures using the JosKn-KleinIFS formula in Mandelbulb 3D. All credit goes to Jos Leys for creating the code, with the help of Knighty, and LucaGN (aka Dark- Beam) for making the Mandelbulb3D formula. First of all it is important to add the JosKn-KleinIFS formula to your M3Formulas folder in the Mandelbulb 3D directory if you haven't already (...\Mandelbulb 3D v1.9.1\M3Formulas). You can find the latest version of the formula here: http://www.fractalforums.com/mandelbulb- 3d/custom-formulas-and-transforms-release-t17106/ (download the .zip file at the bottom of the first post). Once we have added the formula to the program we'll open up our Mandelbulb 3D software. Let's go to the formula tab and select the JosKn-KleinIFS formula in the first formula slot (replace the default Integer Power formula). We'll immediately want to set the Max. iterations to 1 as this will dramatically improve the rendering time. We'll be working in sphere inversion mode. So go ahead and change the Options parameter to 4. We'll also be resetting both the position and rotation parameters. At this point our image should look something like this: To start tweaking the fractal I recommend opening the navigator window and clicking the sideways pointing arrow in the bottom right. This will allow us to tweak the formula parameters using sliders and seeing the results in (quasi) real-time. Using the sliders and seeing what happens will really help you get a better feel for the fractal and will give you a better understanding of which parts of the fractal a certain parameter affects. Now let's start by raising the KleinR parameter to 2. We'll leave invCx at 1 for now but we'll raise invCy from 0.5 to 1. Be sure to play around with sliders and take a good look at what happens when manipulating these parameters (you can set the intensity of the adjustments at the top). You might want to reorient the camera a little bit to get a better view of the fractal. Now we'll start tweaking some very crucial parameters for these types of fractals, BoxSzX and BoxSzY. Tweaking the BoxSzX slider you will see the fractal folding in and out of itself. Especially when lowering the value, we start seeing some more spine-like features. Setting the BoxSzX value to 0.5 will give us a good looking result. Again, we may want to change our camera view to get a better view of the fractal. As we're working with a vertical object, I also decided to change the aspect ratio of the image from 4:3 to 3:4 (you could of course just rotate the fractal instead). Now let's take a look at the BoxSzY parameter. This one really changes the 'texture' of the spheres. Raising the value seems to make the spheres look more empty and clean. Lowering it gives us some more interesting, rougher looking results. Once past the 0.85 mark we seem to lose the "clean" part of the spheres almost completely. 0.8 looks like a good value to me. Another important parameter we haven't looked at is KleinI. Playing around with the slider you can see the "vertebrae" of the spine rotating. After fiddling around a bit I ended up with a value of 0.05. The fractal is now really starting to resemble the shape of a spine. Now we can start fine-tuning some of the parameters until we have a shape we're satisfied with. I ended up raising both invCx and invCy from 1 to 1.1 and lowering KleinR from 2 to 1.986 to get a beautiful saxophone-like shape. All that is left to do now is colouring and lighting this beauty. Here are the parameters of the final spine image: Mandelbulb3Dv18{ g....kV....o0.../....2....ESoFS9fzH6.nHqkI3Ic14EkLXbUM1JPzXN10MhnWC..hBJElqHFr.E ................................Quh4SkVdPz1........A./..................y.2...wD ...Uz6.....0..../MU//......c....8.....E3.....cKCI3h1x8sD/.......B.GT0dkpXm1....U z.....kD12../..........wz.................................U0.....y1...sD...../.. .z1...sD6Io.yb8j/yXGl3ZgtDX2zSTPy3uSfUqjKp.9L7VR0xvkNhnWXwYUz2NL5cUv8upjXo7mlypi bx1ghjBE1AyLzAg7CJBMG3sDU.....21..............sD.6....sD..G..................... .............oAnAt1...sD....z.hgwtdbHjgPu/f9DA........................../....k1. .....4iSoz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52 ...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........2.28.kFrA0. .Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c.. zzzz.............0...................2./8.kzzzD............8.................... /EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq 4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................ E....2..F2E.....I....w....UGjBrGipmGgJKOiZYFH/...............................6U. 0.........E9mqtvbOwzzcNaNaNaNauDzzzzzzzzTzHaNaNaNaNuz.........zD........kz1..... ...8./........zD........E.YaNaNaNaNwzcNaNaNaN4zD...................wz........... ........Uz1.............} {Titel: KleinIFS Spine Tutorial} Turning these spines into starfish shapes is just a matter of manipulating the KleinI parameter. A value of 0.98 really seems to be a sweet spot for a nice starfish shape. But of course there's a lot of other values to be tried out. Use the slider to change the values and see what other interesting shapes you can come up with. The starfish shape may not immediately be apparent after changing the KleinI value to 0.98 from our last image. You will see something like this: The reason for this is that our fractal object has suddenly become a lot bigger, and we need to zoom out quite a bit to get it into full view. I also changed the aspect ratio to 4:3 again. All we want to do now is raise the KleinIters parameter to extend the arms and provide more detail to the empty spheres in the fractal. We now end up with a beautiful starfish-like shape. If you like a more 'spherical' look to your fractal, raise the BoxSzY parameter again. A value of 1 has this result: And there you go, an intricate Kleinian starfish! Have fun experimenting! Starfish parameters: Mandelbulb3Dv18{ g.....h....50.../....2....EGgf2LFdML.TSwpkHO0s6EuE.CkN/b2/gDVmtSVHi7.b9mWfgR3C1k ................................OaNaNaNady1........A./..................y.2...wD ...Uz6.....0..../MU//......01...8.....E3.....IzP28XSPtuD/.......1URj0dkpXm1..... z.EnAnQD12../..........wz.................................U0.....y1...sD...../.. .z1...kD8txVBs6hly1KDgNBbiWEzukpbXgPUUtjlbGWW4OPmxfFZnoc2PYgzEWwt/pxwtsjduSSOM6g LyXGr7wBjFxXz6Qg7mLR83vDU.....YN..............sD.6....sD..G..................... .............oAnAt1...sD....z.hgwtdbHjgPu/f9DA........................../....k1. .....4iSoz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52 ...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........2.28.kFrA0. .Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c.. zzzz.............0...................2./8.kzzzD............8.................... /EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq 4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................ E....2..F2E.....I....w....UGjBrGipmGgJKOiZYFH/...............................6U. 0.........E9mqtvbOwzzkpX0LD8QxyD........Uz1........wz.........zD........kz1..... ...B./........zD........E.YaNaNaNaNwzcNaNaNaN4zD...................wz........... ........Uz1.............} {Titel: KleinIFS Starfish Tutorial} .