How does Chaos game work?

How does Chaos game work?

The goal of the chaos game is to roll the die many hundreds of times and predict what the resulting pattern of points will be. Most students who are unfamiliar with the game guess that the resulting image will be a random smear of points. Others predict that the points will eventually fill the entire triangle.

Who invented the chaos game?

The term “Chaos Game” was coined by Michael Barnsley [1], who developed this ingenious technique for generating mathematical objects called fractals. We have discussed a particular fractal set on this blog: see Cantor’s Ternary Set.

Why does the Chaos Game generate fractals?

The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration.

What is Chaos Game Representation?

Chaos Game Representation is a graphical representation of a sequence. It is a method of converting a long one-dimensional sequence (in our case a genetic sequence) into a graphical form.

Are fractals infinite?

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

Is there a chaotic game?

Chaotic is an out-of-print Danish collectible card game brought to the United States by Chaotic USA and 4Kids Entertainment, and distributed by TC Digital Games. The card game is also featured in the animated series of the same name.

How does turtle work in Python?

turtle is a pre-installed Python library that enables users to create pictures and shapes by providing them with a virtual canvas. The onscreen pen that you use for drawing is called the turtle and this is what gives the library its name.

Is a circle a fractal?

The most iconic examples of fractals have bumps along their boundaries, and if you zoom in on any bump, it will be covered in bumps, etc etc. Both a circle and a line segment have Hausdorff dimension 1, so from this perspective it’s a very boring fractal. There are fractal structures with integer dimension, though.

Do fractals exist in nature?

Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

How do you make a chaotic deck?

How to Make a Chaotic Deck

  1. Determine the number of Chaotic creatures your deck should contain.
  2. Add creature, Mugic and Battlegear cards to the creature deck.
  3. Select five Chaotic location cards from your collection for each three creatures in your creature deck.

How do you play the chaos game?

Play the Chaos Game using the corners of an equilateral triangle as the reference points. Add a starting point at random (preferably inside the triangle). Then add the next point halfway between the starting point and one of the reference points. This reference point is chosen at random.

What kind of fractals does the chaos game generate?

When the length of the jump towards a vertex or another point is not 1/2, the chaos game generates other fractals, some of them very well-known. For example, when the jump is 2/3 and the point can also jump towards the center of the square, the chaos game generates the Vicsek fractal:

When does the chaos game generate the Sierpinski carpet?

When the jump is 2/3 and the point can also jump towards the midpoints of the four sides, the chaos game generates the Sierpinski carpet : When the jump is 1/ phi and the point is jumping at random towards one or another of the five vertices of a regular pentagon, the chaos game generates a pentagonal n-flake :