The above image consist of 400M points and rendered with Houdini internal Karma renderer.
A huge special thanks and lots of gratitude toward my family who kept up with me for so long while I was inside the fractal Flame bubble!
One of the main mission, was to pack the entire algorithm and functionalities I desired inside a tool using only Houdini out of the box. No HDK. As a result, it become a somewhat conservative implementation, it has everything but with some limits as I needed to cut corners everywhere wich became a daunting process to put into balance.
There are more functionalities I'd love to add, but this v1.x is happily out as it is.
A big commitment I needed to honor was to learn how to do fractal art. Building a fractal art tool without knowing what a fractal artist need and feel while doing it is kind of pointless. And so I did so much fractal art with this tool while developing it that I inhevitably fell in love with the discipline. It was important so I could shape and steer this tool in the right direction.
An implementation of FLAM3 inside SideFX Houdini software using Houdini's CVEX programming language. Not a real-time thing but If you have a beefy CPU (dual beefy CPU even better) it will be lots of fun.
The code went up and down and finally settled for the most minimalistic version in favor of performance. The language allowed me to take many shortcuts. He is dealing with execution threading, memory management, and offered me fast, ready to use functions like creating and sampling a cdf, a very robust random number generator and more.
Part of the work is done inside the HDA within the Houdini environment like attribute binding, UI building, parameters creations, their visibility conditions, final compile and much more.
Python has been used to enhance the user experience and to add functionalities like: copy/paste iterators data, load/save palette's libraries, load/save flame's file format, responses/automations to user actions and much more.
FLAM3 for SideFX Houdini generate a live point cloud of the fractal Flame being worked on, witch is the actual render. From there to the final image it is left to the users ( aka points rendering ). With Houdini integrated Karma renderer you will be able to render the generated fractal flames in nearly real time.
Karma viewport renders do not use any density estimator neither any log density display ( a form of tone mapping ) that instead are present in other applications. It does brighten up the high density areas instead ( more points, more bright ) while using the raw color coming from the palette the flame is currently using.
A custom shader could in theory implement a log density display and some form of density estimator.
Karma interactive rendering in the Houdini's viewport.
Highly inspired by Apophysis software and its workflow design.
Many Apophysis fractal Flames are available for download on the web and you can load them inside FLAM3 for Houdini, or you can use Apophysis or Fractorium to author your flames first and load them back into FLAM3 for Houdini. But also the other way around, create your flame in Houdini and render them inside other applications...you've got choises.
Download Apophysis 7x here: Apophysis 7x download
Download Fractorium here: Fractorium download
Imagine the possibilities using Houdini procedural paradigm to control all aspect of your Flame.
FLAM3 for Houdini generate a live point cloud of the fractal Flame being worked on.
Following some images showing FLAM3 for Houdini rendering some of the Fractorium's example flame files. Some have been modified to fit within FLAM3 for Houdini available variations. The screenshots shows Houdini Karma interactive on the left and Fractorium with the same flame file on the right.
Chocolate Scaffold in Too Many Dimensions by plangkye. Source: Fractorium
Mountain by tatasz. Source: Fractorium
Bipolar by tatasz. Source: Fractorium
Flipped disk. Source: Fractorium
Note that all the followings, are also available as PRE_ and/or POST_ variations.
arch auger bent bent2 bipolar blade blob blur boarders bubble butterfly bwraps cell conic cos cosh cosine cot coth cpow crop cross csc csch curl curve cylinder diamond disc disc2 edisc elliptic escher ex exp exponential eyefish fan fan2 fisheye flower flux foci gaussian_blur glynnia handkerchief heart hemisphere horseshoe hyperbolic julia juliaN juliascope lazysusan linear log loonie mobius modulus ngon noise oscope parabola pdj perspective pie point_symmetry polar polar2 polynomial popcorn popcorn2 power pre_blur radialblur rays rectangles rings rings2 scry sec secant2 sech separation sin sinh sinusoidal spherical spiral split splits square stripes supershape swirl tan tangent tanh twintrian unpolar waves waves2 wedge wedgejulia wedgesph whorl
They are 106, if you were wondering...
Fractal flames are really expensive to compute, no wonder GPUs made miracles in this field too.
Being inside Houdini has its major advantages. Only think at the possibilities you have to animate those flames using Houdini's procedural paradigm and toolsets. And the ability to create a pipeline around this tool easily using Houdini's Python HOM libraries.
Karma with the integrated Nvidia Optix denoiser is a great combo to render your fractal images.
CVEX language doesnt have a switch/case constructor, neither any form of pointer functions and such. To get to the selected variation I chained hundreds of if/else if statements. Even tho I partitioned them in the best way I could, this part become a bit of a bottle neck of the entire implementation.
Almost all fractal flame images on my website and instagram use an average of 64 iterations max, some use less and some a bit more. A few exceptions went above 128 and up to 256/512.
Some flames require truly an high amount of iterations to resolve properly.
Below are some presets that Chaotica software ship with, ported inside FLAM3 for Houdini. They have been choosen because they use variations I have implemented too and because some are really expensive to solve.
Some require thousands of iterations to show you the proper results, some of them require hundreds and some others are really quick.
Iterations needed in FLAM3 for Houdini to resolve: 1280
ieddaka gnarl. Author: zuek
Iterations needed in FLAM3 for Houdini to resolve: 512
( potentially a bit less are needed for those but just in case. )
blue modulus. Author: tatasz
lazyswirls. Author: meckie
Iterations needed in FLAM3 for Houdini to resolve: 64
majestic. Author: tatasz
Iterations needed in FLAM3 for Houdini to resolve: 32
blurry splits. Author: tatasz
The following is another preset Chaotica software ship with I truly loved ported inside FLAM3 for Houdini and rendered with Karma renderer.
Iterations needed in FLAM3 for Houdini to resolve: 64
Golden Dragon - Author: meckie
You'll find other scenarios where your iterations number will need to rise up, especially when relying heavily on containers and such.
However from all my tests, betweem 10 and 96 iterations will get you covered on almost all your needs. And dnt forget you can create some beautiful fractal flames with just 6 iterations, I have some of them on my website and instagram.
I could add a lot more functionalities but this project consumed me for a very long time. Every aspects of this algorithm, once understood, look simple on the surface but they all present challenges on their own. It has been quite a crazy ride to pack everyhting inside this implementation.
It is time to park this project for a little bit but I really, really loved the long journey on this topic and I will now for ever love fractal flames as a whole, they are awesome ( and addictive )!
Some of the example flame files I'm using as a proof of correctness and shipped with this implementation are created/authored by some incredible fractal artists using a variety of open source / free apps like Apophysis and Fractorium among the most popular.
Please be sure to check out their gallery:
tatasz, plangkye, Pillemaster, Triptychaos, TyranWave, Zy0rg
Reference A: Github::FLAM3 from Scott Draves and Erik Reckase
Reference B: Github::Fractorium from Matt Feemster
Reference C: Github::Apophysis 7x
Reference D: PDF::The Fractal Flame Algorithm publication