Tag Archives: animated fractal

Lichtenberg Figures in wood.

By TheBackyardScientist.


Neko Time!!! =^_^= Dresden Asisi Panometer

Welcome to another Neko Adventure!

Last week I have been on Dresden, Germany. I went for a scientific conference and I explore a little bit the city… and guess what I found?


Panorama! Actually, this time I didn’t make the Panorama, it was already there. I visited the Asisi Panometer in Dresden.


The Panometer is an exposition where a massive painting arrange in 360º around a tower allows you to see the painting as inside of it. In other words, it’s Google street view handmade.

It seems that Asisi has been doing this exposition for a while, Berlin, Leipzig, Dresden, Everest, Rome… All the time bringing a place to life, either an actual view or an ancient one.


The one in Dresden offers a magnificent view of the city as it was in 1756, with all the people going around in horses, with traders in the streets, boats, farms… all the small details of the painting offer a story to the visitor.


If you have the chance to visit it, don’t hesitate, GO! Or maybe one of the others. I want to visit the one about Rome, it promise to be amazing.

If you want to take a look and see how it looks, I took a panorama for you (click on the image to go).


(Of course, I added this place to the Atlas Obscura ).

That’s all








What? Want more? Isn’t enough? Ba!








Ok, here it is


Neko Time!!! =^_^= matthen

Last week I spend some days in Cambridge performing some experiments at the university,l and as always happens when I go to Cambridge, I learn something new.

This time I came across Matt Henderson blog.


Matt has a mathematics degree by Cambridge University, and he is now working on his PhD on statistical dialogue systems.

He is an unstoppable explorer. His blog is full of experiments and nice mathematical simulations. And here I want to show you which are the ones I like the most. Who knows, maybe a collaboration between us could be possible in the future.

So, here they are.



Basically, if you have particles moving randomly and they are able to become added to a seed, then these random patterns appear. They are close related to chemical reactions and electrical transport. Nice post, with code, and a link to.. Agregation images by Andy Lomas.



Gingerbreadman is a chaotic map. Basically, you select random points in the plane and using very simple equations, you transform the points into new ones. If you repeat it enough times, a figure appears that looks like a Gingerbreadman. And I like this one because I also explore it myself. Remember this?

Iterated Function Systems.


Iterated function systems is a technique to build fractals using transformations of points. It’s similar to the Gingerbreadman map, but with a set of equations that alternate randomly. And I also explore it! Remember the 100 posts post?


Double pendulum.


This was the post that bring me to the blog. The double pendulum is an example of a quite simple chaotic system, it’s only two pendulums linked. In the image on top we can see 2 double pendulums, what the animation want to show is that quite similar initial conditions can evolve into very different evolutions. (I’m working in a nice post about this, but I’m not telling anything more now).



This is an applet to play with iterated functions systems. This one uses the geometrical approach for defining the functions used for performing the iteration. I like it, is quite good. Unfortunately, it’s difficult to repeat successfully patterns.

Create GIF animations with Mathematica.

I don’t like Mathematica, I prefer Matlab or Python, but… who knows, this could be useful.

Animated Optical Illusions.


I saw this effect long ago in a book. I like it. I never had enough time to make anything. But here you can see how it works.

Designing Galleries.


In this post what he wants to show is the importance of designing of buildings. Basically, a good design can help to build a museum where you can visit exactly once each room without crossing with other visitors. Or… if it is a mall, how to design it to make people walk several times into the same point (increasing the showing of that particular shop).

Soap film holes.

The film doesn’t belongs to the blog, but is so amazing…

Shepard scale.

I like this one, is my first sound illusion. Basically, you feel like the scale is getting higher, but it is not.

A Tautochrone (or Brachistochrone if you focus on other property) is a curve where no matter you put a ball on it, it always takes the same time to get to the botom point. I saw many times the Brachistochrone and never realize that it also has this property. I can think of quite funny experiments now for it.


f[x_] := Print[StringJoin[x, FromCharacterCode[{91, 34}],x,FromCharacterCode[{34, 93}]]];
f[“f[x_]:=Print[StringJoin[x,FromCharacterCode[{91, 34}],x,FromCharacterCode[{34, 93}]]];f”]

A quine is a piece of code which is able to print itself. I heard about it before, but it’s the first time I saw one for Mathematica.

And thats all. If you want more, visit his blog. Hope you like it!

NetLogo 01

To be prepared for a post about the Santa -Fe institute, I need to introduce you to this program.

is a program to simulate agent-based models using object-oriented programming. What that mean?

A model based on agents is a model of a system where you suppose the system formed by different entities called agents. A model of a solid made by atoms si an example where the agents are the atoms. Is that all? No. An agent-based model must include agents and rules to interact between them. And mos important, the properties of the system must arise as a collective property of the agents. For example, in the solid, the net magnetization must arise as the interaction between the spins of the individual atoms.

Ok, seems like agent oriented models is more or lees what we have been doing for a long time in some simulations. Why so much noise about this program? Because the object-oriented programming is the way of programming agent-based simulations. What do I mean with that? You can program anything with any language (there is a theorem that grants that), but depending on the task and the language used, the problem became easy or a complete hell. So using object-oriented programming is the easy way of dealing with agent-oriented models.


Go to the webpage, hit download, fill the questionnaire (if you wish you don’t need to fill it), and download and install the program.

Now that you did that, run the program for first time,k it will look something like this.

From here, you are only interested in “Interface” and “code”. Interface is where things happen and where you put buttons and sliders to control your simulation. And also, where the graphics and plots will appear. The code view is where you actually write the code for your simulation.

To start with something easy, go to File>Models Library and we are going to choose….  Chemistry and Physics>Ising.

The Ising model is a classical model for magnetism. In this case, each agent is going to behave like a magnet which can be pointing up or down (dark or bright). The agents randomly will be allowed to change their orientation if that minimises their potential energy respects it’s neighbours. And sometimes, randomly also, they will go into a bad configuration. The principal parameter on this model is temperature. Temperature determines the amount of bad random changes. And the interesting result is that below a certain temperature, the system evolves towards all the agents in the same state, while over that temperature the agents in one state equal the agents in the other state. And that is a good example about magnetic domain formation and Curie temperature.
To run the simulation, push setup-random to initialise  the variables and then go to run it.

Hmmm but this representation of the results is not funny. To make it more funny, we are going to plot the average spin versus temperature. To do it, right click on the plot and hit edit. And now we only need to remove the pen that draws the horizontal line and change ticks for temperature. So now, each time the plot updates with a new point, the new point is going to have temperature as x and average spin as y. You can also change the axis limits to fit better the new data.

logo2And now, just change the plotting-interval to maximum, hit setup-random, go…. and ramp up and down the temperature several times slowly (there is a slider on top to accelerate the simulation).


That process is the equivalent to have a magnetic material and cool it down and heat it up several times. You are going to see that sometimes, when you cool it down, you end with a magnetization different from zero, maybe 1. But above some temperature, the magnetization it’s always zero. Something like this.


That transition temperature is what we call Curie temperature.

Ok, so now with a first example.

Step 1: Help>Look up dictionary This will help you quite a lot.

Step 2: File>New.

Step 3: Create a SETUP button. Right click on a white area and add a button. On the window that appears, writet in the commands area SETUP. And hit ok.

Setp 4 Create a GO button. Rigth click on a white area and add a button. On the window that appears, writet in the commands area GO, select forever. And hit ok.

It will look something like this.


This buttons will execute the scripts located in the CODE area with the names SETUP and GO.

Setp 5 Switch to code area and write the commands to SETUP and GO

Setp 6 We write for setup these lines to create 160 turtles (turtle is the generic name for the agents).

  ;; create 160 turtles at the center pointing at diferent random angles and positions
  ;; with different colors
  create-turtles 160 
  ask turtles [
    setxy random-xcor random-ycor]    
  ;; ticks are used to measure time, how many interactions has pased

Setp 7 In each iteration step we ask turtles with same colors to move closer together.

to GO
  ask turtles [
    ;; In order, each turtle is asked to do something
    ;; In this example we pick a random turtle and compare color with the actual turtle
    let a one-of turtles      
    ;; If the color is the same, as the current one, the current one moves towards that turtle.
  if   color =  [color ] of a [face a fd 1] 

All together will look like this.
Setp 8 With all the steps sccomplished, run the simulation.

Like it? Want more? Ok, one more. I show you how is going my random forest on NetLogo. (Remember my version on OpenProcessing?)