39 votes
Accepted

3D tree in Mathematica?

First, an idomatic, but slow version. ...
Henrik Schumacher's user avatar
36 votes
Accepted

How to make this Dragon Curve?

I think OP may want animation with transition effects. Compare these two effects: Then translation ...
chyanog's user avatar
  • 15.6k
29 votes
Accepted

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 ...
Vitaliy Kaurov's user avatar
27 votes
Accepted

L-System in Mathematica

...
Szabolcs's user avatar
  • 235k
25 votes

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: ...
Vitaliy Kaurov's user avatar
25 votes
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How can I draw sequence of these fractal squares?

How about using ArrayMesh and KroneckerProduct: ...
Carl Woll's user avatar
  • 131k
22 votes
Accepted

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 ...
Simon Woods's user avatar
22 votes
Accepted

How to weave Anni Albers Red Meander carpet?

An attempt: Using CoordinateBoundsArray and FindShortestTour: ...
Syed's user avatar
  • 54.2k
21 votes

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: ...
Mark McClure's user avatar
  • 32.5k
18 votes

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 - ...
VividD's user avatar
  • 3,660
18 votes
Accepted

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. ...
Kuba's user avatar
  • 137k
16 votes

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 ...
C. E.'s user avatar
  • 70.6k
16 votes
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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 ...
Mark McClure's user avatar
  • 32.5k
15 votes

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 ...
Mark McClure's user avatar
  • 32.5k
15 votes

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. ...
wxffles's user avatar
  • 14.2k
15 votes
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How to draw a Pythagoras tree like this

Here is one possibility: ...
J. M.'s missing motivation's user avatar
15 votes
Accepted

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 ...
Simon Woods's user avatar
14 votes
Accepted

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. ...
Conor's user avatar
  • 7,449
14 votes

How to draw a Pythagoras tree like this

Related link: https://mp.weixin.qq.com/s/oz1c3crqgC5WMbUFGxLDMQ https://codegolf.stackexchange.com/questions/25043/i-like-pythagorean-trees/210327#210327 ...
chyanog's user avatar
  • 15.6k
14 votes
Accepted

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. ...
flinty's user avatar
  • 25.3k
13 votes

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 $D_0$ ...
zamazalotta's user avatar
13 votes

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 ...
Mark McClure's user avatar
  • 32.5k
13 votes

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: ...
Ray Shadow's user avatar
  • 7,826
13 votes
Accepted

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 ...
m_goldberg's user avatar
  • 108k
13 votes

Create a simple split tree

One idea is to use Dendrogram on a KaryTree. Here is a function that does this: ...
Carl Woll's user avatar
  • 131k
13 votes

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]
azerbajdzan's user avatar
  • 17.2k
13 votes

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 ...
azerbajdzan's user avatar
  • 17.2k
12 votes
Accepted

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}, ...
KennyColnago's user avatar
  • 15.2k
12 votes

How can I make Sierpinski triangle?

RSolve is for symbolic solution of recurrence equations and is obviously inappropriate here. How could you get a closed form solution when there is a random term ...
Szabolcs's user avatar
  • 235k
12 votes

Using Mathematica to create an H-Tree

Here's a simple-minded implementation based on repeated scaling: ...
J. M.'s missing motivation's user avatar

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