# The Burning Ship Fractal

The Burning Ship Fractal is a slight variant on the Mandelbrot Set Fractal.

The basic Mandelbrot Fractal formula is z=z^2+c. The Burning Ship Fractal formula is z=abs(z)^2+c.

The following image is the standard power 2 Burning Ship Fractal rendered using CPM smooth coloring.

Zooming in to the right antenna part of the fractal shows why it was named the Burning Ship.

The next 3 images change the exponent 2 in z=abs(z)^2+c to 3, 4 and 5.

The same power 2 through power 5 Burning Ships but this time using Triangle Inequality Average (TIA) coloring

The next 4K resolution movie shows a series of zooms into Burning Ship Fractals between power 2 and power 5 colored using CPM coloring

and finally another 4K movie showing more Burning Ship zooms colored using TIA coloring

All of the above images and movies were created with Visions of Chaos.

Jason.

# Visions Of Chaos for Android updated

It took a lot longer than I wanted, but the new Visions Of Chaos for Android v1.0 is now available for download. It is 100% free and ad free.

The main new feature is support for running OpenGL ES shaders on your Android device. There are over 1000 sample shaders included with the app.

So, if you own one of the 85% market share Android devices download the app from the Visions Of Chaos for Android web page or directly from Google Play now.

Jason.

# Multiphase Smoothed-Particle Hydrodynamics

Smoothed-Particle Hydrodynamics (SPH) is a method of simulating fluid flow. It is based on representing a fluid by a large number of discreet (individual) particles. Each particle has properties like position, pressure, density, mass, etc. The particles are fed through a bunch of equations that make them move in a fluid like flow.

If you are a maths nerd then one of the better and recommended papers for SPH fluids is Particle-based Viscoelastic Fluid Simulation.

Multiphase SPH is when you have 2 or more fluids with different densities etc (think oil and water) that flow around each other and clump together.

I have always had a fascination with simulating fluids. Over the years I have tried to understand SPH and have had many failed attempts at writing programs to do it (the basic formulas seem relatively simple, but getting the code to run stable without explosions and crashes is far from simple). Then I found this blog post by Tom Madams that had sample source code. With that I was finally able to get SPH working. It can still be fiddly to find a nice set of parameters to make a nice looking movie, but Tom’s code seems to be a great start. Thanks Tom!!

Multiphase SPH is now available in Visions Of Chaos.

A future release will include 3D support.

Jason.

# Extending Multi-Scale Turing Patterns.

See this post for the original Multi-Scale Turing Patterns that came before these variations.

This post was inspired by a comment from Jonathan McCabe on one of his pictures here. What happens when you add a fluid simulator on top of Multi-Scale Turing Patterns?

I already had a simple 2D fluid simulation in Visions Of Chaos based on Jos Stam’s paper and accompanying source code so after some hacking I managed to incorporate it into each step of the Multi-Scale Turing Patterns steps.

Here is a sample movie using the standard Multi-Scale Turing Patterns method.

And here is the same initial start and parameters but this time including Stam’s stable fluid code at each step. This gives more whispy, hairy and vein like features. It also seems to break the cyclic repetitve nature the turing method alone can lead to. Maybe I like the change, maybe not.

And finally another sample. This time with slightly more agressive fluid, histogram equalization auto-contrast (as the above sample was a bit too grey and washed out for my liking) and a pseudo 3D effect.

I then tried using Perlin Noise as a displacement map to push the grid around.

This sample movie is only using a Perlin Noise displacement map.

This sample uses Perlin Noise and then Stam’s Fluid.

This sample uses Stam’s Fluid and then Perlin Noise.

All of the above six movies were created with the latest version of Visions Of Chaos.

Jonathan still continues to amaze me and recently showed off his latest works like this stunning image.

Click for a full size view.

I hope he shares some of the secrets behind that one. I would love to have a play around with it and add something similar to Visions Of Chaos.

Jason.