Made for 2 players (no computer AI in this initial version). Allows multiple games to be played at the same time to increase the challenge.

100% free and ad free. Search for YOTZ on the Android Market to find it.

Jason.

New features include;
Dictionary support for Dutch, English, French, German, Italian and Spanish.
Word search to help crossword solving and other problems.
Rhyming mode that finds words that rhyme with a specified source word. Great help for poets and songwriters.

This also fixes an issue with the earlier release that caused the app to crash if the anagram source word had spaces in it. Never assume your user will realise anything about input and always check/fix input before running the main processes.

Search for “Anagram Generator” in the Android Market to download and install it for free.

Jason.

These following screenshots show my current statistics.

Search for “Quit Smoking Helper” on the Android Marketplace to install it for free.

Jason.

Next version will support multiple languages and the other features of the Windows version of Anagram Generator.

Available now for free from the Android Marketplace. Just search for “Anagram Generator” and you will find it.

Jason.

In the past I used to keep my latest secrets secret. As a developer writing fractal software (or any other software) you want your application to have those “wow” features that no other app can duplicate.

That was a simple-minded and foolish belief. The entire evolution and progress of the human existance is based on people sharing their knowledge and discoveries.

Fractal Forums (actually there is only the one forum, so maybe it should be Fractal “Forum”) was one of the major things that changed my mind. Seeing people happily sharing ideas and developing them together that lead to incredible discoveries (outside the usual sceintific community and peer-reviewed papers) was a welcome breath of fresh air. The original thread covering how the Mandelbulb was discovered shows this process.

Ever since then I have tried my best to share and explain ideas and it has been a very constructive and inspirational experience. Many a time I have shared a snippet of code with another chaos enthusiast who wanted to implement the same thing in their own code. The majority of the time they are very grateful and usually find a new twist to the code or idea I never would have had. This creates the feedback effect of leading to knew ideas that neither of us could have created before.

With this blog I have tried to change from making it an advert for a new release of Visions Of Chaos into a place I can hopefully help others understand the (relatively) simple maths behind chaos theory related ideas so they can enjoy and understand these principals themselves and (most importantly) come up with new ideas and advance the field.

Before the Internet was out there and when I was originally interested in fractals and chaos I only had books from the library to rely on to try and understand and learn how these ideas worked. The first real inspiration was Gleik’s Chaos that really got me into trying to code software to create those simple things like Mandelbrot Sets and Lorenz Attractors. Since the Internet that has all changed. The incredible result of shared knowledge is mind blowing. Whatever obscure topic you are interested in will be covered by someone else out there. You can usually find PDF versions of important papers on any topic. CiteSeer is an excellent resource when researching papers. If that doesn’t work a Google search for “paper name” pdf will usually find a cached copy somewhere. Sites like Processing.org are brilliant with source code to explain how an idea works.

All of this does lead to attribution. If you do share an idea then it can (and usually will) lead to someone using that idea and (in the worse case) calling it their own. This can be discouraging, but don’t let it get you down. I try my best to cite the original sources when I develop a new bit of code. Everyone likes to know that their knowledge and ideas were appreciated and repsected.

Another sig at Fractal Forums included “I beg of you to enrich others as you have been enriched” and I think that sums it up. Without the vast pool of knowledge out there I would have never been able to add all the features into Visions Of Chaos that I have so far and will into the future.

Share the knowledge.

Jason.

Getting to grips with Android has been an interesting learning process. I was going to setup a post or two about setting up the SDK and writing a basic app framework, but at this stage it would be the blind leading the blind. Once I get some more experience it is something I would like to do.

Jason.

After trying a bunch of the freely available apps I wanted to have a go at programming the device for myself. After a few days of hacking I managed to get the first version of Visions Of Chaos for Android (VocDroid) up and running. Currently it only supports 2D Cellular Automata and 2D Cyclic Cellular Automata.

Here are a few screenshots;

Download it for FREE from the Android Marketplace (search for VocDroid) or click here.

Jason.

I was recently having a few games with a mate of mine over some beers and we both realised how tedious the initial setup phase of the game is (initially drawing up the grid of dots and then filling in the random spots until you reach the “end game” of actually using some strategy to fill in the boxes). So after some hacking I wrote a simple app to generate and print game setups.

The first version makes a “perfect” setup in which every move is going to give the oponent a completed box.

That worked OK, but it came down filling in the single boxes, then the doubles, then the triples etc without any chance for a free move to be found.

If the Perfect checkbox is unchecked then after the initial perfect setup is generated there is a 1 in 4 chance of existing walls being removed. This allows a few free moves before the end game begins.

There has been some extensive analysis into the game and many strategies exist for good gameplay.

I had always played the rule that if you can complete a box you have to. Apparently this is the simpler version of the game and the real rules state you do not have to take a box unless you want to. Playing this version opens up many more strategies (see previous strategies link).

If you want to try the app, grab it here. Single exe, just download and run it. It detects the optimal grid size for your current printer when you start it up.

Jason.

Rule 20955 – Power 6 Mandelbulb

Hybrid Mandelbulb

After the previous encouraging results here and here I had to try the fully extended 32,768 possible permutations of these trig variations.

Theta and Phi are initialised by using

theta:=arctan2(z.y,z.x);
phi:=arcsin(z.z/radius);

The Triplex Algebra power function uses

x=radius*cos(phi)
y=radius*cos(theta)*cos(theta)
z=radius*sin(phi)*cos(phi)

Each of the trig components can be +/- sin/cos phi/theta.

Convert these 15 possible combos into a 15 digit binary number using the following rules for each digit from left to right;
1. 0 for X COS, 1 for X SIN
2. 0 for X Phi, 1 for X Theta
3. 0 for +, 1 for -
4. 0 for Y COS, 1 for Y SIN
5. 0 for Y Phi, 1 for Y Theta
6. 0 for +, 1 for -
7. 0 for 2nd Y COS, 1 for 2nd Y SIN
8. 0 for 2nd Y Phi, 1 for 2nd Y Theta
9. 0 for +, 1 for -
10. 0 for Z COS, 1 for Z SIN
11. 0 for Z Phi, 1 for Z Theta
12. 0 for +, 1 for -
13. 0 for 2nd Z COS, 1 for 2nd Z SIN
14. 0 for 2nd Z Phi, 1 for 2nd Z Theta
15. 0 for +, 1 for -

After letting my PC churn away for a few days I had the results of the 32,768 variations. Here are the 16 I found most interesting and/or unique.

Rule 420

Rule 1334

Rule 1444

Rule 2980

Rule 5101

Rule 5613

Rule 6326

Rule 8575

Rule 8703

Rule 11262

Rule 13246

Rule 16795

Rule 17290

Rule 17856

Rule 20937

Rule 20955

All of these new variations are now avilable in Visions Of Chaos.

Jason.

Rule 388 – Power 4 Juliabulb

Rule 404 – Power 2 Juliabulb

Rule 1328 – Power 4 Juliabulb

Rule 2160 – Power 8 Juliabulb

Rule 2512 – Power 2.9 Juliabulb

After the last success with new Mandelbulb variations I extended the possible search space. These variations are also created from formulas from Tad Boniecki. Three of his variations followed these same basic forms.

See this blog post for all the details of the previous new variations. The only change here is adding a second trig call to the Y component. So now, the possible variants follow the pattern

x=radius*cos(phi)
y=radius*cos(theta)*cos(theta)
z=radius*sin(phi)

Each of the trig components can be +/- sin/cos phi/theta.

Convert these 12 possible combos into a 12 digit binary number using the following rules for each digit from left to right;
1. 0 for X COS, 1 for X SIN
2. 0 for X Phi, 1 for X Theta
3. 0 for +, 1 for -
4. 0 for Y COS, 1 for Y SIN
5. 0 for Y Phi, 1 for Y Theta
6. 0 for +, 1 for -
7. 0 for 2nd Y COS, 1 for 2nd Y SIN
8. 0 for 2nd Y Phi, 1 for 2nd Y Theta
9. 0 for +, 1 for -
10. 0 for Z COS, 1 for Z SIN
11. 0 for Z Phi, 1 for Z Theta
12. 0 for +, 1 for -

This bumps the total possible variations up to 4096. After letting the PC churn away for a few hours I had all possible variations with thumbnails (I have avoided posting all 4096 images to flickr this time).

After deleting the spikey and lathed results this got the count of possibles down to 1288.

Deleting all the assymetrical results got the count down to 266 possibles.

Then comes the difficult part. You get down to a bunch of symmetric bulbs that fall into catagories of similar shapes and styles. Culling down the least interesting out of a bunch of 10 or so very similar images sent me cross eyed. In the end I narrowed 4096 down to 27.

Rule 181

Rule 388

Rule 397

Rule 404

Rule 924

Rule 965

Rule 972

Rule 989

Rule 997

Rule 1328

Rule 1412

Rule 1575

Rule 1841

Rule 1996

Rule 2016

Rule 2017

Rule 2024

Rule 2160

Rule 2161

Rule 2512

Rule 2521

Rule 2537

Rule 2608

Rule 2619

Rule 2969

Rule 2984

Rule 3394

All of these new variations are now avilable in Visions Of Chaos.

Jason.