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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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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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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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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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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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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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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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 ...
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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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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 ...
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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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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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Generate a Padovan Spiral
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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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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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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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 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, ...
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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 ...
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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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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 ...
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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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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 ...
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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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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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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 ...
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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 Hilbert Curve
Given an integer n output the nth iteration of the Hilbert Curve in ASCII using the characters ...
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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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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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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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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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Quicksand (piles)
In this fastest-code challenge, you take a positive integer as input, which represents the height of a sand pile, located at (0,0) on an infinite square grid. For example, if our input is ...
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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 ...
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"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-...
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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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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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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 ...
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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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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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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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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 ...
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Draw this fractal generated by applying Newton's method to cosh(x) - 1
I came across this picture the other day: (Credit to Josep M Batlle I Ferrer)
Your job is to generate this picture. This graph is generated by repeatedly applying newton's method to the graph of:
$$f(...
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Make Some Snow!
Your task: generate a Koch snowflake to the nth depth. You do not need to make a complete Koch snowflake, just one side of the starting triangle. Wikipedia on Koch flakes: https://en.wikipedia.org/...
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Compute this fractal matrix
The unique-disjointness matrix ( UDISJ(n) ) is a matrix on all pairs of subsets of {1...,n} with entries $$ U_{(A,B)}=\begin{cases}
0, ~ if ~ |A\cap B|=1\\
1, ~ ...
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Fibonacci word fractal
The Fibonacci word is a sequence of binary strings defined as:
\$F_0 = \$ 0
\$F_1 = \$ 01
\$F_n = F_{n-1} F_{n-2}\$
The first ...
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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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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 ...
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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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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 ...
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Create a triangle whose colors are determined by the bitsums of coordinates
Write a program that, for any \$n\$, generates a triangle made of hexagons as shown, \$2^n\$ to a side. The colors are to be determined as follows.
We may give the triangle barycentric coordinates so ...
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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-...