This page gives an overview of all the turtles that I have published on Turtletoy.

Click on an image to see the turtle in action.

Light rays bouncing around. #path #pathtracer
Path Path Tracer
I use this pseudorandom number generator in many of my turtles, but I never tested its accuracy. At least it has a mean of ~0.5 and a good-looking histogram. If you know the origin of this code, please let me know.
Pseudorandom number generator
The Unreasonable Effectiveness of Quasirandom Sequences https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/ https://youtu.be/PsGUEj4w9Cc
Quasirandom sequences
This is my entry in the non-existent game competition on Turtletoy. Please select the text input field (guess) and start typing. #hangman #game #handdrawing
Hangman
Turtletoy supports an extra adjustable variable type 'string' by adding 'type=string' in a comment behind the variable declaration. To showcase this additional type, I created a turtle that renders the text from the variable 'message' using different fonts that I converted from the SVG fonts of https://gitlab.com/oskay/svg-fonts #text #font #utility
String input type
Packing paths using a circle-packing algorithm. The path's bounding sphere is used for packing, and a convex hull is used to occlude the lines. Draw your path! #packing #handdrawing #path
Path packing
A tortoise (see: https://turtletoy.net/turtle/102cbd7c4d) with a 'path transform' is used to draw houses, bicycles, and geese. #tortoise #path
A path, a goose & a bicycle
I added a method to the path utility class so you can calculate the distance to a path. This function is slow: it divides all bezier curves into segments and calculates the distance to each segment separately. If you use this distance function in your turtle, you should probably implement some cache.
Distance to path
This turtle uses the naive genetic algorithm from https://turtletoy.net/turtle/2f92cd6aa3 to evolve an initial path to one that matches the 'fittest' path as much as possible. #genetic
Path evolution
Mutate your path!
Path mutation
Turtletoy supports an extra adjustable variable type 'path' by adding 'type=path' in a comment behind the variable declaration. This variable type contains a simple SVG path. When you click on the 'Draw path' toggle in the UI, you can redraw the path on the canvas. #path #utility
Path input type
Gilbert tessellation https://en.wikipedia.org/wiki/Gilbert_tessellation #tessellation
Gilbert tessellation
Code adapted for Turtletoy from https://github.com/isohedral/hatviz An aperiodic monotile David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, 2023 https://cs.uwaterloo.ca/~csk/hat/
Aperiodic Hat Monotiles
It's a bit crowded here. #physics #ragdoll
Crowded
Over the past few months, I have spent some free time developing Dittytoy: an online platform that allows you to create music using a minimalistic javascript API. https://dittytoy.net/ https://dittytoy.net/syntax#envelopes #text #font #dittytoy #adsr
Dittytoy
My take on the Pythagoras Tree. - Symmetry is used to lerp the angle to PI/4 at branches - AngleMod and AngleTest can be used to swap the left- and right-angle at certain depths. https://turtletoy.net/turtle/da47b4247b#rotAngle=0.786,aspect=0.5,symmetry=1,cutOffSize=0.125,drawMode=1,angleModulo=3,tension=0 https://turtletoy.net/turtle/da47b4247b#rotAngle=1.126,aspect=10,symmetry=1,cutOffSize=0.104,drawMode=0,angleModulo=3,tension=0 https://turtletoy.net/turtle/da47b4247b#rotAngle=0.594,aspect=1.001,symmetry=1,cutOffSize=0.104,drawMode=1,angleModulo=0,tension=1 #fractal #pythagor
Pythagoras Tree
A turtle to celebrate the birth of our daughter Kauri.
Kauri
Centripetal Catmull-Rom Splines utility code. #spline #utility
Centripetal Catmull-Rom Splines
A collection of functions that can be used to work with polygons. A polygon is defined by an array of vertices [[x0,y0], [x1,y1], [x2,y2], [x3,y3],...]. #utility #polygons
Polygon Utility
A visualisation of the distance to a Julia set. https://iquilezles.org/articles/distancefractals/ https://en.wikipedia.org/wiki/Julia_set #fractal #juliaset
Smooth Julia set
The Barnsley fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book Fractals Everywhere. https://en.wikipedia.org/wiki/Barnsley_fern #Barnsley #fern #fractal
Barnsley fern
I changed https://turtletoy.net/turtle/fa14c628d4 (by @jurgen) a bit, so it only draws the edges.
Plottable Multi-Scale Truchet
Based on line art by Regolo Bizzi - https://www.behance.net/regolo
Amsterdam
Hexagons everywhere. #hexagons #escher
Hexagons
Spawning hexagons recursively. #hexagon #fractal
Hexagon Fractal
Euler Spiral, based on https://twitter.com/matthen2/status/1249611168265547776 by @matthen2.
Euler Spiral
A simple 2D Physics Engine. Based on work by @MaximeEuziere: * https://github.com/xem/mini2Dphysics/blob/gh-pages/index.html * https://github.com/xem/js1k19/blob/gh-pages/emojysics/index.html #physics
Mini 2D Physics Engine
Based on https://turtletoy.net/turtle/d176924430. The tiles can be filled using an alternating pattern when k is even (again using code from David E. Joyce - https://mathcs.clarku.edu/~djoyce/poincare/). Useful Resources: https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model https://strauss.hosted.uark.edu/papers/hypcomp.pdf https://mathcs.clarku.edu/~djoyce/poincare/ https://www.shadertoy.com/view/3tBGDD #Poincare
Poincaré disk model #2
This is my second attempt at drawing the Poincaré disk model in a turtle. Variation: https://turtletoy.net/turtle/d176924430#n=3,k=5,recursion=7,size=90,centerOffset=0,drawFullGeodesics=1 Useful Resources: https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model https://strauss.hosted.uark.edu/papers/hypcomp.pdf https://mathcs.clarku.edu/~djoyce/poincare/ https://www.shadertoy.com/view/3tBGDD #Poincare
Poincaré disk model #1
Bezier curves are used to generate multi-scale quad or double quad Truchet tiles. Inspired by @revdancatt: https://twitter.com/revdancatt/status/1410268274009456642 Variation: https://turtletoy.net/turtle/913672c491#type=1,minDepth=2,maxDepth=5,subDivChange=0.5,numLines=1,curviness=1 #truchet #bezier
Multi-scale bezier Truchet tiles
Raytraced sphere visualised using the 'curl noise' from https://turtletoy.net/turtle/740f09b88c #raytracer #pixels #rays #curl #noise
Raytraced sphere #5
I am just forking the awesome turtles of @llemarie https://turtletoy.net/turtle/48b30c6521 This one uses the smooth Mandelbrot iteration count formula: https://www.iquilezles.org/www/articles/mset_smooth/mset_smooth.htm I made some changes to the PoissonDiscGrid (using a queue), so I could improve precision without getting incorrect self-intersection tests. #fractal #mandelbrot
Smooth Mandelbrot
Raymarching the beautiful scenes of @llemarie's https://turtletoy.net/turtle/b141d327fc, fed into the https://turtletoy.net/turtle/740f09b88c renderer. #3d #curl #raymarching #hatching
Möbius Ladder and Curl
Procedural fingerprints
Fingerprints
A turtle walking through different curl noise fields.
Mixing Curl Noise Fields
A turtle is walking through a curl noise field.
Curl Noise
This turtle is a combination of "Cubic space division" by Escher and the Droste spiral of "Print Gallery" (also by Escher). Note that I divide by e^(0.05*z) vs the normal divide by z to project the vertices to the screen. This way I make sure the projected grid is a Droste image. #Droste #polygons #3D #Escher
Cubic space division #3
A pretty naive way of circle packing. Circles with a radius > hide_radius are not drawn. #packing
Circle packing #2
Tesselation. Based on work by Åse Balko: https://www.instagram.com/asebalko/ #tesselation #simplex #noise #asebalko
Tesselation #1
Verlet integration is used to simulate cloth. The code is not optimized (and very slow) and self-intersection of the cloth is not prevented. https://en.wikipedia.org/wiki/Verlet_integration #physics #cloth
More cloth
A quick experiment to visualize a 2D Signed Distance Field (SDF) using the Contour Lines utility code from https://turtletoy.net/turtle/104c4775c5 For more 2D SDF functions see: https://www.iquilezles.org/www/articles/distfunctions2d/distfunctions2d.htm #contourlines #sdf #signeddistancefields
2D SDF and Contour Lines
Menger Sponge fractal. I use a slightly modified version of the https://turtletoy.net/turtle/d9ae1fb0bd to collect all partially visible faces of the fractal. A bounding box is added to speed up rendering a bit. #voxels #fractal #MengerSponge
Menger Sponge
Different voxel worlds, rendered using my utility class https://turtletoy.net/turtle/d9ae1fb0bd. #voxels
Voxel Worlds
A Utility class to collect and sort all (partially) visible faces of a voxel world. In this turtle, the faces are drawn using the Polygon Clipping utility code from https://turtletoy.net/turtle/a5befa1f8d. Note that the raycaster shoots rays at a fixed sample density, so small faces can be missed. #voxels #utility
Voxel Ray Caster
A turtle to celebrate the birth of our daughter Esja.
Esja
A method of drawing infinitely many touching circles, based on this tweet https://twitter.com/matthen2/status/1256824725814120448 by @matthen2 and https://youtu.be/sG_6nlMZ8f4.
Touching circles
This turtle uses the https://turtletoy.net/turtle/104c4775c5 utility code to visualize the heightfield of a small island (created using https://turtletoy.net/turtle/6e4e06d42e). Todo: add compass. #contourlines #island #simplex #noise
Contour Lines Island
A small and very unoptimized utility turtle that can be used to calculate contour lines. The ContourLines function will return an array of unsorted line-segments. #contourlines #utility
Metaball Contour Lines
A very simple method to construct a fractal inspired by this tweet: https://twitter.com/CentrlPotential/status/1250172108811927552 by @CentrlPotential. https://en.wikipedia.org/wiki/Chaos_game #fractal #chaosgame
Chaos Game
Grid with way too many sliders.
Grid variations
By using the sine of the simplex noise as height value. #simplex #noise
Simplex Noise Waves
Sheep (Ovis aries) are quadrupedal, ruminant mammals typically kept as livestock.
Sheep
A compact Simplex Noise implementation in javascript. Based on: http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf by Stefan Gustavson. #utility #simplex #noise
Simplex Noise
Verlet integration is used to simulate cloth. The code is not optimized (and very slow) and self-intersection of the cloth is not prevented. https://en.wikipedia.org/wiki/Verlet_integration #physics #cloth
Cloth
Another utility class that can be used to draw clipped polygons. #polygons #utility
Stars
A small and simple Dungeon generator. The algorithm used to generate the structure is far from perfect: you will find a lot of hidden (=not connected) rooms. Better procedural dungeons can be found here: https://watabou.itch.io/one-page-dungeon Change the seed-value for other randomly generated dungeons. #procedural #hatching
Turtle Dungeon
Dyson hatching (https://dysonlogos.blog/), based on a blog-post by Oleg Dolya (https://www.patreon.com/posts/hatching-in-1pdg-31716880). A complete Dungeon Generator is next ;-) #hatching #possion-disc
Dyson Hatching
Bezier curves are used to generate quad, double quad, double triangle or hexagon Truchet tiles. #truchet #bezier
Bezier Truchet tiles
My first Truchet tiles experiment. #truchet #hexagon
Hexagon Truchet
A tortoise (see: https://turtletoy.net/turtle/102cbd7c4d) with a 'spiral transform' is used to draw houses, bicycles, and geese. #tortoise
A tortoise, a goose & a bicycle.
A spiral of points is created. Each i^th point is rotated by an angle i*2*PI*Ratio around the origin. The initial value of the Ratio is 0.38196601125 (which gives the "golden angle"). You can change the Ratio using the slider below. A better explanation about what's going on can find here: https://youtu.be/sj8Sg8qnjOg. The final Voronoi diagram is based on the Delaunay triangulation of the points, using delaunator of Mapbox: https://github.com/mapbox/delaunator #Delaunay #triangulation #voronoi
Voronoi Spiral
Points of the raytraced scene are found using the same algorithm as used in: https://turtletoy.net/turtle/7367ba3a0c. All points are connected using Delaunay triangulation. A Voronoi is created based on these triangles. I have used the Delaunay triangulation implementation of Mapbox: https://github.com/mapbox/delaunator #raytracer #pixels #rays #Delaunay #triangulation #voronoi
Raytraced sphere #5
A naive genetic algorithm is used to reconstruct the quote: "Natural selection is anything but random." by Richard Dawkins. The chance that a random sequence of 41 characters matches the quote is 1 : 95^41 ≈ 1 : 10^80. #text #genetic
Natural selection
Exactly the same turtle as "Cube cityscape #1" (https://turtletoy.net/turtle/789cce3829), but the turtle is drawn by a Tortoise using a wave-transform (see: https://turtletoy.net/turtle/102cbd7c4d). Different at every Compile & Run. #city #polygons #3D #transform #tortoise
Cubic cityscape #2
Another small utility class. The Tortoise class extends the Turtle class by adding support for transforms. A transform is a function that maps an input [x,y] coordinate to a transformed [x', y'] output coordinate. #transform #tortoise
Transforms
A small utility turtle that can be used to print text to the screen. #text #font #utility
Hello, world
Verlet integration is used to simulate a simple ragdoll. https://en.wikipedia.org/wiki/Verlet_integration #physics #ragdoll
Ragdoll physics
Example to show how you can use adjustable variables; a new and experimental feature. You can use the sliders below to adjust the Fractal binary tree (https://en.wikipedia.org/wiki/L-system#Example_2:_Fractal_(binary)_tree). #fractal #lsystem
Adjustable fractal tree
A collection spirographs (https://en.wikipedia.org/wiki/Spirograph) #spirograph
Spirographs
A turtle Quine. It should be possible to create much smaller turtle Quines by using a compact font and more efficient compression algorithms for the data. (similar to my Shader Quine https://www.shadertoy.com/view/MlGcRz) #quine
Quine
Reimplementation of Edward Zajec’s “Il Cubo” from 1971. Based on the images from http://www.edwardzajec.com/tvc4/pil1/index.html (I don't speak Italian).
Il Cubo
Based on: https://martinmcbride.org/post/generative-art/cardioid-string-art/
Cardioid
Grow pattern based on Poisson-Disc Sampling. Based on work by @FogleBird: https://medium.com/@fogleman/pen-plotter-programming-the-basics-ec0407ab5929. #possion-disc
Poisson- Disc Grow Patterns
A quite famous torus. I have combined code from @flockaroo (https://turtletoy.net/turtle/2dc4806767) and the cleaned-up version of my own occlusion code by @ge1doot (https://turtletoy.net/turtle/c2cf454d80).
Torus
Points of the raytraced scene are found using the same algorithm as used in: https://turtletoy.net/turtle/7367ba3a0c. All points are connected using Delaunay triangulation. I have used the Delaunay triangulation implementation of Mapbox: https://github.com/mapbox/delaunator #raytracer #pixels #rays #Delaunay #triangulation
Raytraced sphere #4
I have ported most of "ln, The 3D Line Art Engine" by Fogleman (@FogleBird) to javascript, so it can be used on Turtletoy. Not all code is ported and not all code-paths are tested: probably there are still (a lot of) bugs left. This Turtle is a port of the example: https://github.com/fogleman/ln/blob/master/examples/function.go
3D Line Art Engine: Function
I have ported most of "ln, The 3D Line Art Engine" by Fogleman (@FogleBird) to javascript, so it can be used on Turtletoy. Not all code is ported and not all code-paths are tested: probably there are still (a lot of) bugs left. This Turtle is a port of the example: https://github.com/fogleman/ln/blob/master/examples/skyscrapers.go
3D Line Art Engine: Skyscrapers
I have ported most of "ln, The 3D Line Art Engine" by Fogleman (@FogleBird) to javascript, so it can be used on Turtletoy. Not all code is ported and not all code-paths are tested: probably there are still (a lot of) bugs left. This Turtle is a port of the example: https://github.com/fogleman/ln/blob/master/examples/csg.go
3D Line Art Engine: CSG
I have ported most of "ln, The 3D Line Art Engine" by Fogleman (@FogleBird) to javascript, so it can be used on Turtletoy. Not all code is ported and not all code-paths are tested: probably there are still (a lot of) bugs left. This Turtle is a port of the example: https://github.com/fogleman/ln/blob/master/examples/outline.go
3D Line Art Engine: Outline
I have ported most of "ln, The 3D Line Art Engine" by Fogleman (@FogleBird) to javascript, so it can be used on Turtletoy. Not all code is ported and not all code-paths are tested: probably there are still (a lot of) bugs left
3D Line Art Engine: Spheres
Path tracer code from https://turtletoy.net/turtle/50b8079a52 combined with the 'circle packing dithering' from https://turtletoy.net/turtle/7367ba3a0c. #raytracer #pixels #rays #dithering
Cornell Box #2
Somebody had to... I have created a path tracer to render the Cornell Box (https://en.wikipedia.org/wiki/Cornell_box). Ray trace code base on the (excellent) book "Ray tracing in one weekend" (http://in1weekend.blogspot.com/2016/01/ray-tracing-in-one-weekend.html) by Peter Shirley (@Peter_shirley). The code is simplified for this specific scene, and I have added direct light sampling to reduce noise. #raytracer #pixels #rays #dithering
Cornell Box #1
I have combined the raytraced scene of https://turtletoy.net/turtle/11075dfee0 with the circle-packing algorithm of https://turtletoy.net/turtle/f9915c1d89 to get some sort of dithering. #raytracer #pixels #rays #dithering
Raytraced Sphere #3
A first experiment to draw a procedural city of cubic building blocks. The city will be different each reload / re-compile. Try out different options by changing the settings at the top of the code. In a next turtle, I will clean up and optimize the code and add more variety to the buildings. #city #polygons #3D
Cubic cityscape #1
A study in rotating shapes.
Rotating shapes
Based on Cubic space division by Escher: https://www.wikiart.org/en/m-c-escher/cubic-space-division. Cubic space division 1: https://turtletoy.net/turtle/4487884a96 #polygons #3D #Escher
Cubic space division #2
Based on Cubic space division by Escher: https://www.wikiart.org/en/m-c-escher/cubic-space-division. #polygons #3D #Escher
Cubic space division #1
Testing my polygon-clipping algorithm of https://turtletoy.net/turtle/92ebe08d89 more. #polygons
Polygon weaving
I have added a (slow) hatching option to the polygon routines of https://turtletoy.net/turtle/348e597fd8. #polygons #Escher
Polygon hatching
The first test of a (very naive) algorithm used to calculate the visible parts of the line segments of a polygon that is (partly) occluded by other polygons. The algorithm doesn't work well with edge cases (overlapping lines or polygons that share one or more vertices). I tried to come up with a function that would give me a set of non-overlapping lines, so I can draw the result directly with my plotter. #polygons
Polygon clipping
Some Lissajous curves: https://en.wikipedia.org/wiki/Lissajous_curve
Lissajous curves
Experiment to create something that looks like a hand drawing. Based on https://turtletoy.net/turtle/b0ac9de176 and https://turtletoy.net/turtle/f9915c1d89. #handdrawing #packing
Smile!
A minimal SVG parser to draw a 🐢. #SVG
Turtle
Based on https://turtletoy.net/turtle/f9915c1d89 but an imperfect imperfect-poly-draw-function is used to draw the 'circles'. The result is very imperfect. #packing #handdrawing
Imperfect poly packing
A probably pretty naive way of circle packing. Circles with a radius > hide_radius are not drawn. #packing
Circle packing #1
Fractal plant by Paul Bourke: http://paulbourke.net/fractals/lsys/ #fractal #lsystem
Fractal plant #2
Fractal plant: https://en.wikipedia.org/wiki/L-system#Example_7:_Fractal_plant #fractal #lsystem
Fractal plant #1
https://en.wikipedia.org/wiki/L-system#Example_5:_Sierpinski_triangle #fractal #lsystem
Sierpiński arrowhead curve
A raytraced scene is rendered by drawing (a lot) of circles with increasing radius for each pixel. The amount of circles depends on the brightness of the corresponding circle. #raytracer #pixels #rays
Raytraced Sphere #2
A raytraced scene is rendered using randomly placed strokes. The length of a stroke is inversely proportional to the brightness of the corresponding pixel of the raytraced scene. #raytracer #pixels #rays
Raytraced sphere #1
An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar: https://en.wikipedia.org/wiki/L-system. #fractal #lsystem #snowflake
L-System
Dragon curve example. #fractal #dragoncurve
Dragon curve