# Tag Info

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### 3D tree in Mathematica?

First, an idomatic, but slow version. ...
Accepted

### How to make this Dragon Curve?

I think OP may want animation with transition effects. Compare these two effects: Then translation ...
• 15.6k
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### Sampling "nice" mandelbrot sets?

Excellent question. First I show the result where fractals are sorted from more to less "nice" or "interesting" by going from left to right and top to bottom. This is obvious to the naked eye. In my ...
• 73.1k
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• 235k

### How to make this Dragon Curve?

A simple way to make Dragon Curve is using AnglePath. Define a function that generates points for the Dragon curve: ...
• 73.1k
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### How can I draw sequence of these fractal squares?

How about using ArrayMesh and KroneckerProduct: ...
• 131k
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### Fractal basins of attraction in a Magnetic Pendulum

JM commented: If you want to try things out, use Nylander's second snippet, which is using a Beeman integrator. This looks to be faster than native NDSolve[] for this specific case. Paul ...
• 85k
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### How to weave Anni Albers Red Meander carpet?

An attempt: Using CoordinateBoundsArray and FindShortestTour: ...
• 54.2k

### Converting a Sierpinski tetrahedron to a Graph

A natural and simple way to approach this problem, assuming that your SiPyramid function has been defined, is as follows: ...
• 32.5k

### Inverted version of Sierpinski triangle

Yes, as the other people noted, this geometric transformation called inversion is just mapping coordinate $r$ in a polar coordinate system onto the coordinate $1/r$ (the other coordinate - angle - ...
• 3,660
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### Animate Koch curve generation and include a transition effect

Isn't the fastest but there is not much to see for higher iterations anyway. Let me know if anything is unclear. ...
• 137k

### Fractal basins of attraction in a Magnetic Pendulum

I don't have any breakthrough ideas, but I am able to cut the computation time in half on my computer by optimizing the usage of NDSolve. My version of your code ...
• 70.6k
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### The correct way to draw this fractal

I see five types of squares that all move to the next step differently: We start with 1 square of type 0 that produces four squares at level 1. Each of those produces three squares at level 2, none ...
• 32.5k

### Construction Steps of Barnsley's Fern

I've got a package that makes dealing with iterated function systems pretty easy. You can download it off of my webspace. That package implements both deterministic and stochastic alorithms to ...
• 32.5k

### I would like to create a fractal by copying, scaling and rotating the initial element

We could do this with rules. It's slightly complicated because it's not a simple recursion. Consider the coloured image in the question. The green element fractals into the three blue elements. ...
• 14.2k
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### How to draw a Pythagoras tree like this

Here is one possibility: ...
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### Speediest Julia Set "By Hand"

Plotting a million points is rather slow, instead you can use Image. This requires the results in a 2D array, so remove the ...
• 85k
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### Construction Steps of Barnsley's Fern

After playing with the variables in a Manipulate I came up with these numbers for the arguments of the AffineMap functions. ...
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• 15.6k
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### Diploria labyrinthiformis - can we reproduce Ernst Haeckel's drawing of a brain coral?

Not quite there, but this could be a basis for a better answer that does a line sweep along the B-Spline. ...
• 25.3k

### Measuring fractal dimension of natural objects from digital images

"Can we improve the box-counting method?" Most certainly. But first of all, it is important to point out that if you are only checking if a box is empty or not you are effectively measuring the $D_0$ ...
• 271

### Interactive Mandelbrot Zoomer?

Here is a less quick and dirty version that includes a few more features. To zoom in, you simply click and drag to select a rectangle. Generally, you've got to hit the ...
• 32.5k

### Using Mathematica to create an H-Tree

Iterative version Each horisontal line generates two vertical lines of the same length, while each vertical line generates two horisontal lines, which are twice shorter: ...
• 7,826
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### Create a simple split tree

I like recursion so I've written a recursive solution. Helper function for doing the drawing the basic u-shaped element of the tree ...
• 108k

### Create a simple split tree

One idea is to use Dendrogram on a KaryTree. Here is a function that does this: ...
• 131k

### How can I draw sequence of these fractal squares?

ArrayMesh/@SubstitutionSystem[{1->{{1,0,1},{0,1,0},{1,0,1}},0->Table[0,3,3]},{{1}},5]
• 17.2k

### Reproduce the annulus fractal

There is some bug in ConicGradientFilling if more than 2 colors are used. (see line at right of each annulus) Bellow are images ...
• 17.2k
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### Fractal plotting for the Collatz fractal

One way of coding the iterations may be defined as follows. The function CollatzFractal01[z0] returns a list {Abs[z],iter}, ...
• 15.2k