chaotic attractor explorer

Αρκετές σχετικά απλές εξισώσεις που παρουσιάζουν χαοτικές ιδιότητες, δίνουν πολύ όμορφα γραφήματα. Έφτιαξα το chaotic attractor explorer για να εξερευνήσω αυτά τα γραφήματα, και τώρα μπορείτε να τα εξερευνήσετε και σείς, χρησιμοποιώντας το. Θα χρειαστεί οπωσδήποτε να διαβάσετε τις οδηγίες, αλλά το αποτέλεσμα θα αξίζει τον κόπο.

Πολύ σημαντική πηγή έμπνευσης και πληροφοριών ήταν το site του Paul Bourke.

Το chaotic attractor explorer είναι freeware, το χρησημοποιείτε με δικιά σας ευθύνη.

 

Quite a few relatively simple chaotic equations give wonderful graphs when plotted. I built the chaotic attractor explorer to explore those graphs, and now so can you, by using it. You will need to read the instructions below, but it will be worth it.

Very important source of information and inspiration during this project for me has been Paul Bourke's excellent fractals site.

The chaotic attractor explorer is freeware, use at your own risk.

 

download here (600k)

the following is the readme file, as included with the program to give you a better idea of how it works:

chaotic attractor explorer
- by aristides mytaras
www.mytaras.com
www.mytaras.com/chaos.html

this is a program that enables users to change the variables in 15 sets of chaotic equations so as to experience, explore and create some wonderful graphical representations that can be made with equations with strange attractors.

before you begin, check out the presets, by pressing ] to load them sequentially right after you load the program.

V changes the equation number. equations 13-15 use 4 variables, the others use only the first 3.
Z clears the screen
C changes background-foreground color - from black to white.
X changes info display.
TAB grabs a screenshot and stores it into the application folder - be sure to hide the interface with X, or it will be included in the screenshot!
ENTER randomizes the 4 variables according to the equations selected.
B toggles between the 3 drawing types - DRAFT appears fast but all pixels are the same color, FINE makes a point brighter as it gets used more, COLOR1 goes through some colors so you can see the direction in time.
/ key changes display type, NORMAL is, well, normal, then there is X-time graph, Y-time graph and LINES connects the dots with lines.
T-G increments - decrements the delay between ploting 2 points. normal is zero delay. this can be used to better visualise some graphs.

ARROW KEYS move the view.
-,+ buttons (next to zero) zoom in and out
SPACE pauses

keys 1-9 change the STEP of increment. for example, 1 means step of 0.1, 2 means step of 0.01, 3 means step of 0.001 etc until 7. 8 means step 1, 9 is a step of 10 and 0 is step of 100.

Q-A increments- decrements variable c1 according to STEP
W-S increments- decrements variable c2 according to STEP
E-D increments- decrements variable c3 according to STEP
R-F increments- decrements variable c4 according to STEP

for example, pressing 2 to set the STEP to 0.01 and then pressing E increments c3 by 0.01. after that, if you press F, c4 is decremented by 0.01 etc etc.

N animates the last used variable towards the last used direction, by STEP. for example, if the previous move was W, it will be c2 that will be animated incrementing by STEP. all parameters can be changed DURING animation, like STEP, variable, direction, even draw type, etc.
Y-H increments - decrements the number of points plotted (iterations of the equations) for each frame of the animation. default is 15000.
N stops the animation.

[ key saves a preset in the gallery folder. this is not a screenshot. ALL variables are saved, including animation state.
] key loads the next preset from the gallery folder.

about the equations: the first equation set [1] is from a small basic program by philip ham. equations [7] and [8] are x-y and x-z representations of the famous lorentz equations. equation set [11] is clifford attractors, set [14] is peter de jong attractors.

 

pictures:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

www.mytaras.com