知名度低そうなシェルピンスキーのギャスケットの作り方

1. 真っ黒！

2. 右下を白にする

3. 各黒い区間の右下を白にする

4. 繰り返す

5. 繰り返す

6. 繰り返しまくる！

終わり。

どうでもいいけど、こいつ（n→∞）の面積は0らしいね。面白い。

関連

おまけ

JSのコード

const canvas = document.querySelector("canvas");
const context = canvas.getContext("2d");
canvas.width = 800;
canvas.height = 800;

const count = 10;

draw();

function draw() {
    context.fillStyle = "black";
    context.fillRect(0, 0, canvas.width, canvas.height);

    let blockList = [{
        color: "black",
        startX: 0,
        startY: 0,
        width: canvas.width,
        height: canvas.height
    }];

    for (let i = 0; i <= count; i++) {
        let tmpBlockList = [];
        for (const block of blockList) {
            if (block.width < 2 || block.height < 2) {
                i = Number.POSITIVE_INFINITY;
                break;
            }
            drawBlock(block);
            if (block.color === "black") {
                tmpBlockList = tmpBlockList.concat(splitBlock(block));
            }
        }
        blockList = tmpBlockList;
    }
}

function splitBlock(block) {
    const {startX, startY, width, height} = block;

    const width1 = Math.floor(width / 2);
    const width2 = width - width1;
    const height1 = Math.floor(height / 2);
    const height2 = height - height1;
    const startX1 = startX;
    const startX2 = startX + width1;
    const startY1 = startY;
    const startY2 = startY + height1;

    return [
        {color: "black", startX: startX1, startY: startY1, width: width1, height: height1},
        {color: "black", startX: startX2, startY: startY1, width: width2, height: height1},
        {color: "black", startX: startX1, startY: startY2, width: width1, height: height2},
        {color: "white", startX: startX2, startY: startY2, width: width2, height: height2},
    ];
}

function drawBlock(block) {
    if (block.color === "black") {
        return;
    }
    context.fillStyle = "white";
    context.fillRect(block.startX, block.startY, block.width, block.height);
}