Mandelbulber Animation

Nanoworld: a Mandelbulb fractal and a sphere primitive

I finally tried the animation feature of the Madelbulber2 fractal surfaces software. From the "View" menu, if you select "Show animation dock" then you are provided with the following controls:

animation controls

For my first animation I set the lower drop-down menu (speed control) to "constant".

"primitives" settings

To create a fractal surface for the animation, I started with a "primitive", a sphere, in the default position (0,0,0) and with the default radius (1). See the "primitives" controls shown to the left. When combined using the union(or) function, this sphere "covered up" part of the default-sized Mandelbulb fractal surface so only the "high altitude" parts of the fractal surface were visible. See the "Nanoworld" image above.

First Humanoid

I used the default material, but selected the image shown to the right for use as a "color texture". You can see that humanoid face "looking out" from the surface of Nanoworld.

In order to make a fractal surface with some interesting features such as tunnels, I combined the following four fractal surfaces (using the "union(or)" method) with the sphere primitive:

I decided to zoom in on the archway (upper left)

1) Mandelbulb
2) Reimann - Sphere Msltoe
3) Box Fold Bulb Pow 2 V2
4 Msltoe - Toroidal Bulb

To render this fractal surface, I used the "Delta DE" method for estimating distances from the camera to the fractal surface.

As a starting point for my animation, I zoomed in on the surface of Nanoworld, just in front to the arched entryway that can be seen "from above" in the image to the left. Some of the images that I show here have been modified in Photoshop so as to include characters from the Grean's Hack series.

Looking through the first archway,
another archway is seen beyond.

For creating the path that would be followed by the moving camera in order to create the animation, I used a low image resolution (half of the smallest preset resolution: 360 x 240 pixels) and a value of 1.0 for the "raymarching" render quality parameter. I clicked on the "record flight path" button and used the mouse cursor to guide the camera through the archway. Each frame for the animation took just a few seconds to render on these low-resolution settings. Then I switched to a larger image size (720 x 480) and 0.1 for the raymarching parameter before clicking "render flight animation". I generally make still renderings at my computer's screen resolution (1920 x 1080 pixels).

The video above shows a raw animation made with Mandelbulber2 and the default Mandelbulb fractal only. Shown below is a longer video, made by combining several animation sequences into tunnels present in the more complex fractal surface described above. The second video (below) was made with iMovie and includes some transition scenes that were made with Photoshop. This second video has an audio track supplied by YouTube: "The Quantum  Realm". For some of the animation sequences, there were 180 degree turns. The default animation settings in Mandelbulber2 for camera momentum and maximum rate of camera movement make it hard to turn the camera quick enough, so I changed those settings at the risk of making the camera a little wobbly as I went through the series of tunnels.

Shown below is a single rendered frame close to the second archway and processed with Photoshop to insert Artep into the scene.

The second archway is cluttered with "alien lifeforms". Artep was added to the scene with Photoshop.

looking back towards the first archway

According to the instructions for Mandelbulber2, I thought that holding down the "shift" key would stop the camera from advancing forward and allow me to turn the camera. However, I could not get that to work.

The image to the right shows the view looking back towards the first archway from the second archway. This image was modified in Photoshop to add some lighting and to add in the two story characters. Without the added lighting, the inside of the archway was rather dark.

Sadly, the instruction manual for Mandelbulber2 does not have a section describing how to use the keyframes feature for animations. At six hours of rendering for a 5 second animation I'm afraid that I'm reaching the limits of this old computer.

 

image source

The video above is an example where I could rotate the camera ('z' and 'x' keys) and control speed of the "flight" with left and right mouse buttons.

Related Reading: other posts in this series about using Mandelbulber2 to make fractal surfaces
- 7 Fractal Surfaces
- Hybridize 7
- 7 Alternate Iterations -

Next: the origins of Mary

visit the Gallery of Movies, Book and Magazine Covers

visit the Gallery of Posters

7 Alternate Iterations

Figure 1. Top image: plain "JosLeys-Kleinian V2".
Lower 4 panels: see the KEY to the left.

This is the third in a series of blog posts about how I am using  Mandelbulber2 software to create background images for my science fantasy story, "Final Change".

When hybridizing fractal surfaces, the default algorithm (used here) is to give equal priority to each equation that is combined. However, sometimes you want to retain the general features of a fractal surface and modify it slightly. This can be accomplished using the Mandelbulber2 settings for how many iterations to do sequentially for each fractal equation and when to start including each fractal in the iterations performed.

Iteration controls that are available
while hybridizing fractal equations.

The images to the right illustrate how the "JosLeys-Kleinian V2" fractal was given extra priority while allowing it to be hybridized with some other fractals.

KEY. Modifying fractals:
1) "Box Fold Bulb Pow 2"
2) "Riemann - Sphere Msltoe V1"
3) like #2 plus "Ides" fractal
4) like #3 plus the Box Fold fractal

Figure 2. Four versions using the "JosLeys-Kleinian V2" Fractal.
Top: "JosLeys-Kleinian V2" hybridized with three other fractals.
2nd from top: "JosLeys-Kleinian V2" plain, default render
3rd from top: "JosLeys-Kleinian V2" plain, "Delta DE" rendering
Bottom: "JosLeys-Kleinian V2" hybridized with two other fractals.

The examples in Figure 1 were all rendered with the default method for determining distance from the camera to the fractal surface. However, using the "Delta DE" distance method makes a significance change in the appearance of the rendered "JosLeys-Kleinian V2" fractal, as shown in Figure 2.

In the image to the left (Figure 2), the third version from the top shows the default rendering for "JosLeys-Kleinian V2". Just above that is the rendering with "Delta DE" which gives more detail and you can see that there is a thin yellow thread connecting between the tips of the two largest copies of the basic fractal surface.

In Figure 2, the uppermost version of the surface was made by hybridizing the 4 fractals mentioned above (for Figure 1) with 5x preference to "JosLeys-Kleinian V2" and the "Ides" fractal delayed until the other three had already gone through 2 steps of rendering in the iteration process. Also rendered with the "Delta DE" method.

The bottom version in Figure 2 was made without using "Box Fold Bulb Pow 2" and only the other three fractals. The "Riemann - Sphere Msltoe V1" fractal was given twice as many iterations as the "Ides" fractal. This version was rendered with the default "analytical" distance method.

These examples in Figures 1 and 2 were made using the default material and the "lightmap" color texture previously mentioned here.

For the ending of "Final Change", I want an illustration for nanoville, the part of the Writers Block where nano-scale femtobots reside.

Figure 3. In the nanorealm.

I added one more fractal equation for "Quaternion" and that gave me what I imagine to be a nanoscopic domain where femtobot replicoids can reside (Figure 3).

For "Final Change", only two of the many residents of nanoville are carried over into the Final Reality. I'd like to be able to depict a hierion field surrounding and protecting these two replicoids in a space-time bubble of physiotime.

Related Reading: animated fractals 

Next: the conclusion of "Final Change"

visit the Gallery of Movies, Book and Magazine Covers

Hybridize 7

Spire Mountain, a hybridized Mandelbulb
surface. Bottom panel: "Add Constant 4D".

This is my second blog post about using Mandelbulber2 software to create fractal surfaces. Here, I'll use the surface shown to the right ("Spire Mountain") as an example.

Mandelbulb surface example

For this example, I started with the basic Mandelbulb surface that is built into the software and the default material. The image to the left shows that starting fractal surface.

You can select among the available transform functions and begin reshaping the core fractal shapes.

Add Constant 4D transform

An example of a transform function is "Add Constant 4D".

You can manually enter the four parameters (x, y, z, w) or you can use an available randomizer pallet.

randomize

If you click on the randomize button then a new window opens that can be used to generate a desirable transform. An example of the pallet with some computer-generated random transforms is shown below:

A random selection of transform parameters is generated then you can select among them.

In the example shown above, I used the "medium randomization" option. From among the pallet of generated options, I selected the variant shown below:

Left, standard Mandelbulb surface. Right, the transformed surface made with "Add Constant 4D".

The effect of this transform function on the Spire Mountain hybrid surface is shown in the image at the top of this page.

To transform the standard Madelbulb surface into Spire Mountain, I went through the sequence of hybridization steps shown below:

I started with the standard Madelbulb fractal surface (inset, upper left) then six other fractals (their names are shown) were added sequentially and hybridized to produce the next modification of the surface (red arrows).

As shown below, I then zoomed in on the top half of Spire Mountain.

I liked the spire with the radiating folds. Further zoom:

I then moved the camera down and to the right, entering one of the valleys. I changed the camera angle to point at the base of the spire:

Left panel: default. Right panel: with new light source.

In the image to the right, the left panel is a quick, low resolution render. In general, the default lighting is good, but you can zoom in on some poorly lit parts of the surface.

I made my first extra light source inside one of the dark depressions. Just below the main render window is a drop-down menu that allows you to change what clicking in that window does. One option is to insert a new light source. The panel on the right ⇛ is a higher quality rendering with the added light source.

Another mode for using the cursor allows you to determine how far it is from the current camera position to a point on the surface of the fractal.

As shown to the left, you can move the cursor over the fractal surface and obtain the coordinates for points that are on the surface. The software calculates the distance from the current camera position to the point on the surface that you select with the cursor.

This distance information is useful for making decisions about how far to move the camera when you want to zoom in on the surface. If you are not careful, you can zoom in too far and move the camera inside the fractal!

For the science fantasy story that I am currently writing,  "Final Change", I wanted an illustration of an entrance leading into the highest chamber of Seelie. I zoomed in on the lower part of Spire Mountain...

Left: bottom center part of Spire Mountain. Right: after Photoshop processing.

Related Reading: Mandelbulber2 iteration controls

Next: High Seelie

visit the gallery of fractals

7 Fractal Surfaces

imaginary book cover
The fractal surface used for the background
in this scene was made using the boolian "union"
option for combining multiple fractal equations.

I've been playing with Mandelbulber2, software that allows for making images that contain three dimensional fractal surfaces. I've been running the software on an old (2011) Macintosh (64bit, 2.5 GHz quad core) and have not been annoyed by long render times.

Fantasyland
I started using Mandelbulber2 when I wanted to create some background images for scenes in High Seelie. Seelie is a space-time bubble in the Hierion Domain that is home to the sy'Paz, alien-human hybrids that were constructed as a tool for Interventions into Earth's timeline.

Not wanting the artificial environment of High Seelie to look like Earth, I'm using Mandelbulber2 to create backgrounds for scenes such as the one shown to the right on this page.

the approach to Mount Seelie
and Joanna's cave

That imaginary book cover (above) is meant to depict Joanna MacDonald at the entrance to her physics research lab. The high mountain location of Joanna's secluded laboratory is illustrated to the left.

These two imaginary book covers for my story "Final Change" were made using Photoshop. For "Mount Seelie", I combined parts of three different fractals and the image of a fashion model.

fractal surface, example #1

That "mountain" scene was mostly derived from the fractal surface shown in the image to the right. Using the Mandelbulber2 software, you can zoom in on small parts of a fractal surface.

Top panel: default distance estimation calculations.
Bottom panel: using "Delta DE" distance estimation.
fractal surface, example #2

I've usually been content to use the default image quality settings of the software. However, when I first made my depiction of Joanna's cave, I was not satisfied with the alien plant life that was growing near the cave entrance.

As shown to the left, when I changed the setting for distance estimation (the distance from the "camera" to the fractal surface) to "Delta DE", the results were better. According to the instruction manual, using Delta DE takes longer, but in this case it was fast and gave me a more detailed, plant-like surface for the "ground" that Joanna is standing on.

This shows the control setting for "Delta DE".

For the rest of the "cave", I preferred the results obtained using the default distance estimation method which created a smoother and glossier cave-like surface.

The third fractal that I used to make the cover image for "Mount Seelie" is shown below. All three of these fractal surfaces were made by mixing together from 3 to 5 different built-in fractal-generating formulas that come with the software. Those formulas are part of the pallet of options that allow for the creation of a wide range of different fractal surfaces.

In "Final Change", the red "face" is used as Joanna's intercom system which she uses to screen visitors arriving at her laboratory.

a three dimensional fractal surface made by the Mandelbulber2 software -  fractal surface, example #3

Materials

three examples of materials

Mandelbulber2 comes with several different predefined "materials" that define properties such as the luminosity and glossiness of the rendered fractal surfaces.

So far, I have mostly used the default material and sometimes made adjustments to the color pallet as needed for a particular scene.

One of the more interesting fractal surfaces is the "pseudo Kleinian": 

This image was made using the Mandelbulbe2 "pseudo Kleinian" fractal surface formula and the "copper" material. Note the reflections, particularly in the upper right. -  fractal surface, example #4

see

The image above (example #4) reminds me of a steampunk beer brewery.

Below are two examples of fractal surfaces made with the "colored glass" material. The first (example #5) is the default color setting, the second example (#6) is with a modified set of parameters:

Above: default "colored glass" material-  fractal surface, example #5

custom colors for the "colored glass" material-  fractal surface, example #6

selecting a color texture

flying through a chamber of Seelie

I also rendered the "pseudo Kleinian" fractal formula using the "water" material. You can add a "color texture" to materials, as shown in the image to the left.

To the right is an imaginary book cover cover that I made depicting one of the high chambers of Seelie. The pre-photoshop rendering is shown below.

This image was made using the Mandelbulbe2 "pseudo Kleinian" fractal surface formula and the "water" material. The colors were modified by using the "lightmap" texture. -  fractal surface, example #7

hybrid

Eye candy.

Related Reading: more discussion of Mandelbulber2

Next: "Zeptites of Seelie"

visit the Gallery of Movies, Book and Magazine Covers