# Questions tagged [fractal]

Fractals are shapes that are self-similar and are usually quite detailed. Well-known fractal sets include the Mandelbrot set, Julia sets, and Phoenix sets. Tree-like fractal drawings are also common.

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### Sierpinski Carpets

Who doesn't love a good fractal? The Sierpinski Carpet is a classic example of a fractal. To complete this task, you will be required to generate a carpet of type $n$ and print the resulting image ...
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### Graphical Representation of Koch Snowflake

Generate a Koch Snowflake A Koch snowflake is a triangle that for each n, another equilateral point is added in the middle of each side: http://en.wikipedia.org/...
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### Draw the Devil's Staircase

The Devil's Staircase is a fractal-like function related to the Cantor set. Your task is to replicate this funky function — in ASCII art! Input A single integer ...
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### Mandelbrot image in every language

I always used a Mandelbrot image as the 'graphical' version of Hello World in any graphical application I got my hands on. Now it's your guys' turn. Language must be capable of graphical output or ...
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### ASCII Cayley Graph

While doing some research for a different challenge I'm formulating, I came across a Cayley graph, specifically this one. Since I'm one of the top ascii-art challenge writers, of course I had to make ...
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### Generate Newton fractals

You all know the Newton method to approximate the roots of a function, don't you? My goal in this task is to introduce you into an interesting aspect of this algorithm. Newton's algorithm converges ...
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### Unicode T-square

Challenge Create a function or program that, when given an integer size, behaves the following way: If size is equal to 1, ...
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### Draw a Dragon Curve

You task for today: draw a dragon curve! In case you don't know what a Dragon Curve is, here is an introductory ViHart video (Really cool, please watch!) Your task: draw a dragon curve, iterated at ...
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### Eye test - How many squares are in this picture?

The picture: Sick of the same old grid where the answer is simply a square pyramidal number? Accept the challenge and write a program that given a positive integer $n$ counts how many squares are ...
915 views

### The Image of the Dragon

I saw a cool gif of the twin dragon curve made from a square, and wondered what would happen if we started from another base image. So I wrote a program to do this.      &...
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### Print a Cantor Set

The Challenge Build a N-Leveled Cantor Set. The Cantor ternary set is created by repeatedly deleting the open middle thirds of a set of line segments. The program receives one parameter ...
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### Draw A Sierpinski Triangle

The Sierpinsky Triangle is a fractal created by taking a triangle, decreasing the height and width by 1/2, creating 3 copies of the resulting triangle, and place them such each triangle touches the ...
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### Draw the Hilbert Curve

A Hilbert Curve is a type of space-filling curve, and it basically maps a line to a plane. Each point in the line corresponds to just one point in the plane, and each point in the plane corresponds to ...
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### The Cantor Function

The Cantor function is continuous everywhere and constant almost everywhere, but has an average slope of 1: The function can be found recursively: $f_0(x)=x$ \\$f_{n+1}(x)=\left\{\begin{matrix}\frac{...
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### Help, I'm trapped in a Sierpinski triangle!

Drawing the Sierpinski triangle has been done to death. There's other interesting things we can do with it though. If we squint hard enough at the triangle, we can view upside-down triangles as nodes ...
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### Fractal Cathedral

Given a positive integer n >= 1, output the first n rows of the following structure: ...
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### Create an "H" from smaller "H"s

Challenge Create a function or program that, when given an integer size, does the following: If size is equal to 1, output ...
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### The IHIH Pyramid

I find it fascinating how the letters "H" and "I" are very similar. "H" is a horizontal stroke surrounded by two vertical strokes; "I" is a vertical stroke surrounded by two horizontal strokes (...
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### Hilbertize an image

For a computer vision app I want to do a mapping of an image, in such a way that every pixel fit hilbert curve, instead of conventional layout. So task could be as follows: Task description Given ...
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### Generate a mandelbrot fractal [closed]

Your task is to draw the mandelbrot set in ascii. It should look something like The complex number c lies in the mandelbrot set, when the sequence ...
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### Drawing the Peano curve

Introduction In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit ...
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### ASCII art H trees

An H tree is a fractal tree structure that starts with a line. In each iteration, T branches are added to all endpoints. In this challenge, you have to create an ASCII representation of every second H ...
573 views

### Generalized Cantor set segment lengths

Problem Let's define a generalized Cantor set by iteratively deleting some rational length segments from the middle of all intervals that haven't yet been deleted, starting from a single continuous ...
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### Generate TeX to typeset Sierpinski Triangle Fractal

Challenge Write code that outputs TeX (LaTeX) math-equation code (given below) that will typeset Sierpinski Triangle Fractal of 5 levels. Shortest code wins. Details TeX (and friends like LaTeX, ...
990 views

### Draw a Fractal in Under 200 Characters [closed]

After noticing all the fractal submissions/questions, I thought it would be fun to start a contest where everyone submits their favourite fractal. The Contest Generate a fractal in under 200 ...
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### ASCII Hilbert Curve

Given an integer n output the nth iteration of the Hilbert Curve in ASCII using the characters ...
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### Binary tree fractal

Today's challenge is to draw a binary tree as beautiful ascii-art like this example: ...
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### ASCII Dragon's Curve

Introduction The Dragon's Curve is a fractal curve that notably appears on section title pages of the Jurassic Park novel. It can very simply be described as a process of folding a paper strip, as ...
711 views

### ASCII art square affine fractals

Write the smallest program you can to create affine fractals. You may use any method you feel like that generates the same results as the rules below. You don't have to use any ideas from the ...
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### Draw the Hilbert curve using slashes

The Hilbert curve is a space filling fractal that can be represented as a Lindenmayer system with successive generations that look like this: Thanks to http://www.texample.net/tikz/examples/hilbert-...
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### Generate fractals from bit patterns in ASCII

Overview Write a program that prints out simple fractal patterns given a bit pattern encoding the fractal, plus the per-generation scale factor of the fractal and number of generations. Explanation ...
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### Computer Generated Cracked Soil

Write a program that takes in an integer from 0 to 65535 (216-1) and generates a unique 500×500 pixel image that looks as similar as possible to these 6 real life images of cracked soil: These ...
868 views

### Make a 2d menger sponge [duplicate]

A menger sponge is a fractal made out of cubes within cubes within cubes... If you start with a cube, on each face there are 9 squares. The middle square becomes empty (or 0). The other 8 squares ...
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### ASCII L-system renderer

Background An L-system (or Lindenmayer system) is a parallel rewriting system that, among other things, can be easily used to model fractals. This question concerns deterministic, context-free L-...
964 views

### Gasket Weaving - draw a Sierpiński knot

Given an integer N >= 2, produce an image showing a Sierpiński knot of degree N. For example, here are knots of degree 2, 3, 4 and 5: Click on the images to view full size (the higher the degree the ...
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### Sierpinski Layers

Starting with /\ you can create a Sierpinski triangle like pattern by adding a line beneath such that... Any loose branch / or <...
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### The strange attraction of the logistic map

The purpose of the challenge is to approximately plot the attractor of the logistic map as a function of its parameter r (also called bifurcation diagram), or a subregion of it. The appearance of the ...
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Introduction Similar to the Fibonacci Sequence, the Padovan Sequence (OEIS A000931) is a sequence of numbers that is produced by adding previous terms in the sequence. The initial values are defined ...
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### Hilbertify an image

I like the Hilbert Curve. Your task for this challenge is to take an image (strictly a square image where all the sides are a power of two pixels wide) and unravel it line by line in a zig-zagging ...
444 views

### Make Some Snow!

Your task: generate a Koch snowflake to the nth depth. You do not need to make a complete Koch snowflake, just one side of the starting triangle. Wikipedia on Koch flakes: https://en.wikipedia.org/...
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### Koch Snowflake - codegolf

The Koch snowflake (also known as the Koch star and Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in ...
586 views

### Build the blancmange function

The blancmange function is used as an example in basic calculus of a function that is continuous everywhere, but differentiable nowhere. It achieves this effect by using the sums of ever-diminishing ...
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### Is it within the Cantor set?

The Challenge For this challenge, you are supposed to determine if a given number is in the Cantor set. So first, let's define the Cantor set. First, start with the numbers between 0 and 1. Any ...
376 views

### It's factors all the way down!

This challenge is inspired by this fantastic animated diagram (thanks to flawr for posting it in chat). Given an input n, draw all of its prime factors as nested ...
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### Draw the Serpinski Triangle [duplicate]

For today's fractal challenge, draw at least 5 iterations of Sierpinski's triangle! (Shown below is Sierpinski's trinagle) The resolution of the image must be sufficent that the smallest triangles ...
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### ASCII Art of the Day #2 - Flow Snakes

A Flow Snake, also known as a Gosper curve, is a fractal curve, growing exponentially in size with each order/iteration of a simple process. Below are the details about the construction and a few ...
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### Computer Generated Textured Wall Paint

The paint on the walls in my room has a random, almost fractal-like, 3-dimensional texture: In this challenge you will write a program that generates random images that look like they could be part ...
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### Create a fractal tree

What I would like to see is a fractal tree being drawn where the you can input an integer, and the output will be a fractal tree with the entered amount of branch steps. Rules: The fractal should be ...