Small fractal in Codea

Saw a video of this, just wanted to try it out in codea. Touch the screen to set the start point of the algorithm.

function setup()
    viewer.mode = FULLSCREEN
    mid = vec2(WIDTH/2, HEIGHT/2)
    v = vec2(0, 200)
    pts = {
        mid + v,
        mid + v:rotate(math.rad(125)),
        mid + v:rotate(math.rad(-125))
    }
    noSmooth()
    background(0)
    --pts = {}
end

function draw()
    for i, p in ipairs(pts) do
        rect(p.x,p.y, 2,2)
    end
    if #pts > 3 then
        local p = pts[#pts]
        local p2 = pts[math.random(1,3)]
        pts[#pts] = p + (p2 - p) * .5 
        rect(p.x,p.y, 2,2)
    end    
end

function touched(t)
    if t.state == ENDED then
        table.insert(pts, t.pos)
    end
end
2 Likes

Hah that’s amazing

There is way too little code there to produce that result. So clever

Nice! Reading the code, I think it is the Sierpinski triangle. Am I right?

Experimented with adding color, for the heck of it:

-- SmallFractal by tnology
function setup()
    viewer.mode = FULLSCREEN
    mid = vec2(WIDTH/2, HEIGHT/2)
    v = vec2(0, 200)
    pts = {
        mid + v,
        mid + v:rotate(math.rad(125)),
        mid + v:rotate(math.rad(-125))
    }
    noSmooth()
    background(0)
    --pts = {}
end

function draw()
    if #pts > 3 then
        local p = pts[#pts]
        local p2 = pts[math.random(1,3)]
        pts[#pts] = p + (p2 - p) * .5 
        fill(math.random(255), math.random(255), math.random(255))
        rect(p.x,p.y,3,3)
    else
        for i, p in ipairs(pts) do
        fill(math.random(255), math.random(255), math.random(255))
        rect(p.x,p.y, 3, 3)
            end
    end
end

function touched(t)
    if t.state == ENDED then
        table.insert(pts, t.pos)
    end
end

@UberGoober - that really is neat, and so short. Found by tapping around the perimeter it fired up dots so Inbuiltbup a star field around it. Do all of those tapped spots potentially build more fractals ?

Dunno! Not super clear how the code works, just wanted to add some variety :wink:

Yes, it as random walk that creates Sierpinski triangle. Even if you start outside the triangle, or in the middle, it will quickly move to create dots within the triangle pattern.

@tnlogy by chance I’ve been tinkering around with your old terrain generator



Terrain = class()

function Terrain:init(x)
    local d,s = 2000,20
    self.d, self.s = d,s
    self.m = mesh()
    for y=-s,s do
        for x=-s,s do
            self.m:addRect(x*d,y*d,d,d)
        end
    end
    self.m.texture = readImage("Cargo Bot:Crate Yellow 1")
    self.m.shader = S
    self.m:setColors(
    color(119, 60, 49, 61))
end

function Terrain:draw(pos)
    self.m.shader.light = vec3(math.cos(ElapsedTime),
    math.sin(ElapsedTime),1):normalize()
    pos =vec2(pos.x, pos.z)
    local step = self.d*(self.s+.5)*2
    local o = vec2(math.floor(pos.x/step+.5),
    -math.floor(pos.y/step+.5))
    
    -- drawing a 3x3 grid centered at camera position
   -- for y=-1,1 do --tnology's original values
      --  for x=-1,1 do
    for y=-5, 5 do --boosting these to 5 makes it go much farther in the distance
        for x=-5, 5 do
            pushMatrix()
            local u,v = (o.x+x)*step,(o.y+y)*step
            translate(u,v,0)
            self.m.shader.offset = vec2(u,v)
            self.m:draw()
            popMatrix()
        end
    end
end

Perlin = [[
//
// Description : Array and textureless GLSL 2D simplex noise function.
    //      Author : Ian McEwan, Ashima Arts.
    //  Maintainer : ijm
    //     Lastmod : 20110822 (ijm)
    //     License : Copyright (C) 2011 Ashima Arts. All rights reserved.
    //               Distributed under the MIT License. See LICENSE file.
    //               https://github.com/ashima/webgl-noise
    // 
    vec3 mod289(vec3 x) {
        return x - floor(x * (1.0 / 289.0)) * 289.0;
    }
    vec2 mod289(vec2 x) {
        return x - floor(x * (1.0 / 289.0)) * 289.0;
    }
    vec3 permute(vec3 x) {
        return mod289(((x*34.0)+1.0)*x);
    }
    float snoise(vec2 v)
    {
        const vec4 C = vec4(0.211324865405187,  // (3.0-sqrt(3.0))/6.0
        0.366025403784439,  // 0.5*(sqrt(3.0)-1.0)
        -0.577350269189626,  // -1.0 + 2.0 * C.x
        0.024390243902439); // 1.0 / 41.0
        // First corner
        vec2 i  = floor(v + dot(v, C.yy) );
        vec2 x0 = v -   i + dot(i, C.xx);
        // Other corners
        vec2 i1;
        //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0
        //i1.y = 1.0 - i1.x;
        i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0);
        // x0 = x0 - 0.0 + 0.0 * C.xx ;
        // x1 = x0 - i1 + 1.0 * C.xx ;
        // x2 = x0 - 1.0 + 2.0 * C.xx ;
        vec4 x12 = x0.xyxy + C.xxzz;
        x12.xy -= i1;
        // Permutations
        i = mod289(i); // Avoid truncation effects in permutation
        vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 ))
        + i.x + vec3(0.0, i1.x, 1.0 ));
        vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0);
        m = m*m ;
        m = m*m ;
        // Gradients: 41 points uniformly over a line, mapped onto a diamond.
        // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
        vec3 x = 2.0 * fract(p * C.www) - 1.0;
        vec3 h = abs(x) - 0.5;
        vec3 ox = floor(x + 0.5);
        vec3 a0 = x - ox;
        // Normalise gradients implicitly by scaling m
        // Approximation of: m *= inversesqrt( a0*a0 + h*h );
        m *= 1.79284291400159 - 0.85373472095314 * ( a0*a0 + h*h );
        // Compute final noise value at P
        vec3 g;
        g.x  = a0.x  * x0.x  + h.x  * x0.y;
        g.yz = a0.yz * x12.xz + h.yz * x12.yw;
        return 130.0 * dot(m, g);
    }
]]


S = shader(Perlin .. [[
uniform mat4 modelViewProjection;
attribute vec4 position;
attribute vec4 color;
attribute vec2 texCoord;
uniform vec3 light;
uniform vec3 pos;
uniform vec2 offset;
varying lowp vec4 vColor;
varying highp vec2 vTexCoord;
varying lowp float vShade;

float h(vec2 p) {
p = p + offset;
return snoise(p*.001)*20. +
snoise((p-vec2(1.,1.))*.0001)*1000. +
snoise((p-vec2(1.,1.))*.00002)*5000.;
}

vec3 cnormal(vec2 p) {
float d = .01;
float h1 = h(p-vec2(d,0.)) - h(p+vec2(d,0.));
float h2 = h(p-vec2(0.,d)) - h(p+vec2(0.,d));
vec3 v = cross(vec3(d*2.,0.,h1),
vec3(0.,d*2.,h2));
return normalize(v);
}

void main() {
vColor = color;
vTexCoord = texCoord;
vec4 p = position;
p.z = p.z + h(p.xy);

if (light != vec3(0.,0.,0.)) {
    lowp vec4 nor = vec4(cnormal(p.xy),0);
    vShade = (dot(nor.xyz,light)+0.2)/1.2;
    if (vShade >1.0) {vShade=1.0;}
    if (vShade <0.2) {vShade=0.2;}
} else {
    vShade = 1.;
}
gl_Position = modelViewProjection * p;
}
]], [[
uniform lowp sampler2D texture;
varying lowp vec4 vColor;
varying highp vec2 vTexCoord;
varying lowp float vShade;

void main() {
lowp vec4 res = texture2D(texture, vTexCoord);
lowp vec4 c = vColor;
c.rgb = c.rgb * vShade;
gl_FragColor = c;
}
]])

In your original project you had it auto-scrolling under the viewer, generating new pieces as needed. Do you think the same process you use here would be possible in Craft?

@UberGoober I haven’t used Craft at all, but I guess it would be possible? Nice to see that my now 11(!) year old code is used. :slight_smile:

1 Like