Under the Hood of Dashboard Baby

I recently published a fractal animation named Dashboard Baby that also illustrates the capabilities of my fractal animation software prototype.

The creation process took over a month from the first animation draft to the final release and we exchanged a number of versions of both the animation and the soundtrack with Dj Tabora.

Interpolating Fractal Details

My previous post introduced brushes and the background flow field that are the main visual components of the application. I’ve also developed a method to smoothly adjust the level of detail of a fractal based on the contents of the flow field.

You can see this varying level of detail in use throughout the animation. Most of the time there are more details on the areas that I’ve painted with brushes. Just before the outro scene you can see how the painted areas begin to show less details than the peripheral areas. This is reverted back during the final outro scene.

The image below illustrates the idea of interpolating iterations.

$The fractal set is shown for iterations ranging from 8 to 14. The flow field contents used to interpolate between iterations is shown at bottom left. Black corresponds to 8 and white 14 iterations. The bottom right image shows smoothly interpolated iterations using the flow field on the left.$

The fractal set is shown for iterations ranging from 8 to 14. The flow field contents used to interpolate between iterations is shown at bottom left. Black corresponds to 8 and white 14 iterations. The bottom right image shows smoothly interpolated iterations using the flow field on the left.

A couple of mathematical tricks were needed to hide the iteration boundaries and make the interpolated result look smooth. I’ll discuss these tricks and provide the associated CG shader source code on a later post.

The Ducky Nova Fractal

The following presumes you are familiar with computing fractals, so buckle up and watch out for equations. The fractal set used throughout Dashboard Baby is available for Ultra Fractal (UF) with the name Nova Ducky. It combines a convergent fractal known as Nova with a mirroring feature that has been used in a number of UF formulas labeled as Ducky. The fractal set is generated by iterating the function

$\hat{z}_{n+1} = z_n - R \frac{z_n^2-1}{2z_n} + C$

$z_{n+1} = |Re \; \hat{z}_{n+1}| + |Im \; \hat{z}_{n+1}| i$

where $R$ and $C$ are complex parameters called relaxation and seed, respectively. The outro scene uses values $R = (3.3, 2.68)$ and $C=(-2.6, 6)$ . New iteration values $z_{n+1}$ are given by the componentwise absolute value of $\hat{z}_{n+1}$ .This flips negative components back to the positive top right quad of the complex plane, which gives rise to the symmetrical supercharged kaleidoscope appearance characteristic to Ducky/Talis fractals.

Here’s an upr for Ultra Fractal users from the final scene of Dashboard Baby.

 DashboardBabyFinalScene {  
 fractal:  
  title="Dashboard Baby Final Scene" width=960 height=540 layers=1  
  credits="Kevin Kerttunen;11/19/2013"  
 layer:  
  caption="Background" opacity=100  
 mapping:  
  center=8.7076952615/-0.451219253 magn=0.94692544 angle=-81.0557  
 formula:  
  maxiter=15 percheck=off filename="jh.ufm" entry="jh-NovaDuckyJulia"  
  p_bailout=1E-20 p_power=2/0 p_relaxation=3.3/2.68 p_seed=-2.6/6  
  p_symmetryMode=Abs p_absOffset=0/0  
 inside:  
  density=2 transfer=linear filename="jh.ucl"  
  entry="jh-InverseDistanceToPoint" p_point=0/0 p_offset=0  
 outside:  
  transfer=linear  
 gradient:  
  comments="Simple grayscale gradient." smooth=yes rotation=-200  
  index=10 color=16448508 index=51 color=5002588 index=87 color=0  
  index=204 color=2961975 index=-157 color=5792620 index=-94  
  color=10003372  
 opacity:  
  smooth=no index=0 opacity=255  
 }