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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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: ...
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0answers
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Abacabadabacaba [duplicate]

I recently stumbled on the fractal word abacabadabacaba..., which is a 67 million letter word according to a pattern. The full word is actually the 26th word in a series as follows: A aBa abaCaba ...
10
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1answer
227 views

Recursive Steiner Chains

Steiner Chains are a set of N circles where each circle is tangent to 2 other non-intersecting circles as well as the the previous and next circles of the chain, as seen in the below images: In ...
26
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1answer
372 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 ...
14
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7answers
755 views

Draw an indexed fractal

Introduction In this challenge, a 2×2 matrix is indexed like this: 0 1 2 3 We define a family of fractal-like patterns F(L), where L is a length-n list of these indices and F(L) has size 2n-...
26
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4answers
532 views

Map string to Hilbert curve

Let's map some strings to 2d space, fractal style. Your task is to compute a Hilbert curve and lay a string along it. Task The task is to take the single-line input string, and lay it out along a ...
42
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2answers
2k views

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 ...
16
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6answers
626 views

Converging Sums of a Fractal Sequence

Background A fractal sequence is an integer sequences where you can remove the first occurrence of every integer and end up with the same sequence as before. A very simple such sequence is called ...
10
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3answers
277 views

Generate Toothpick Sequence

What is Toothpick Sequence? According to Wikipedia In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed by repeatedly adding line segments ("...
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0answers
177 views

ASCII Art Sierpinski Triangle [closed]

Introduction Your challenge is to create a program that prints an ASCII art Sierpinski triangle given an input on the size. Challenge The program will need to take an input of a number and output ...
11
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2answers
305 views

Beta's Snowflake

Challenge Winter is fast approaching with many places receiving the first layers of snow for the 15/16 season, so why don't we break out the snow machines and code ourselves some snow? Given a ...
30
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9answers
1k views

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 ...
19
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3answers
668 views

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 ...
31
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9answers
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ASCII Art of the Day #2 - Flow Snakes

I came across this really nice snow-flake like ASCII fractal by Michael Naylor [citation needed but not found]. Just like a fractal, it grows exponentially in size with each order/iteration. Below are ...
9
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1answer
455 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 ...
9
votes
1answer
107 views

Determine whether rational coordinates are in the right Sierpinski triangle

The Sierpinski triangle is a set of points on the plane which is constructed by starting with a single triangle and repeatedly splitting all triangles into four congruent triangles and removing the ...
4
votes
1answer
427 views

Word fractal plotter

Iterated Function Systems An Iterated Function System (IFS) is a method of constructing self-similar fractals. Each fractal is defined recursively as the union of several copies of itself, with each ...
12
votes
2answers
418 views

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-...
13
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4answers
814 views

Draw a Random Walk with Slashes

Write a program or function that takes in a positive integer N (via stdin/command line/function arg) and prints or returns a string representation of a two dimensional random walk that is N steps long,...
44
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16answers
5k views

Sierpinskified Code

Write a rectangular block of text that when arranged into a Sierpinski carpet, using same-sized blocks of spaces for the empty portions, creates a program that outputs the iteration number of the ...
44
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21answers
8k views

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 n >= 0, indicating the size of ...
11
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4answers
289 views

H Tree Directories

Programmers are often obsessed with drawing fractals. I think we need a new computer based medium. The H tree is a fairly simple type of fractal made of horizontal and vertical lines. Here it is at ...
45
votes
3answers
4k views

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 ...
12
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11answers
2k views

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/wiki/Koch_snowflake#Properties We ...
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17answers
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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 and print the resulting image to ...
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1answer
692 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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12answers
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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 \ splits again into two branches: /\. Any collision of branches \/ dies ...
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4answers
2k views

Draw an Apollonian Gasket

Given three mutually tangent circles, we can always find two more circles which are tangent to all three of those. These two are called Apollonian circles. Note that one of the Apollonian circles ...
21
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10answers
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Play the Chaos Game

The Chaos Game is a simple method to generate fractals. Given a starting point, a length ratio r and a set of 2D points, repeatedly do the following: From your set of points, pick one at random (...
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5answers
2k views

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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28answers
9k views

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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8answers
3k views

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 ...
3
votes
3answers
341 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 ...
18
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5answers
4k views

“Sorry, young man, but it's Turtles all the way down!”

Execute a Lindenmayer System A Lindenmayer System (or L-system) is related to Thue and Post systems, and is used in botanical modeling and fractal generation. An L-system is described by string-...
33
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27answers
9k views

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 ...
10
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9answers
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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 N (a ...
39
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27answers
4k views

Generate a mandelbrot fractal?

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 function z = z^2 + c remains bounded, z starts at 0. For ...
19
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2answers
3k views

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 ...
18
votes
7answers
2k views

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 ...