🖼️ 图片工具Image Tools （第 4 页）(page 4)
科赫分形（雪花 / 反雪花 / 折线）Draw a Koch Fractal
绘制科赫分形：雪花（外凸）、反雪花（内凹）或单条科赫折线。可调迭代、画布、线宽、填充与方向，导出 PNG，本地完成。Draw a Koch fractal: snowflake (outward), anti-snowflake (inward) or a single Koch polyline. Set iterations, canvas, line width, fill and orientation; export PNG locally.
莱维 C 曲线分形Draw a Lévy Fractal
绘制莱维 C 曲线：每条边换成两条成直角的边，反复迭代形成 C 形。可调迭代与颜色，导出 PNG。Draw the Lévy C curve: replace each edge by two right-angled edges and iterate into a C shape. Set iterations and colours; export PNG.
海威龙分形（折纸龙）Draw a Heighway Fractal
绘制海威龙（折纸龙）曲线：经典 L 系统龙形曲线，可调迭代、线宽与颜色，导出 PNG。Draw the Heighway dragon (paper-folding) curve via its classic L-system. Set iterations, line width and colours; export PNG.
双海威龙分形Draw a Twin Heighway Fractal
绘制双海威龙：两条海威龙曲线拼成的空间填充图案，可调迭代与颜色，导出 PNG。Draw the twin Heighway dragon: two dragon curves joined into a space-filling pattern. Set iterations and colours; export PNG.
三角龙分形Draw a Triangle Dragon Fractal
绘制三角龙（terdragon）曲线：每条线段换成三段、转 120°，是海威龙的三角变体，可调迭代与颜色，导出 PNG。Draw the triangle dragon (terdragon): every segment becomes three with 120° turns, a triangular variant of the Heighway dragon. Set iterations and colours; export PNG.
豪斯多夫分形（H 树）Draw a Hausdorff Fractal
绘制 H 树（豪斯多夫树）：每一步画一个 H 形（或旋转 90° 的工字形），再在它的四个端点上画边长减半、方向转 90° 的同样图形，反复铺满正方形。可调迭代、方向与颜色，导出 PNG。Draw an H-tree (Hausdorff tree): each step draws an H (or the same shape turned 90°, like an I-beam), then a half-size copy turned 90° on each of its four tips, filling a square. Set iterations, orientation and colours; export PNG.
T 方形分形Draw a T-Square Fractal
绘制 T 方形分形：大正方形四角再叠更小的正方形，反复形成十字/T 状结构。可调迭代与颜色，导出 PNG。Draw a T-square fractal: smaller squares on the corners of a larger one, repeating into a cross/T structure. Set iterations and colours; export PNG.
冰晶分形（弗罗斯蒂）Draw a Frosty Fractal
绘制冰晶风分形（Cesàro 折线）：类似科赫曲线，但把 60° 的尖角换成可调的折角（默认 90° 直角），形成霜花般的折线。可调迭代（1–9）与折角（10–170°），导出 PNG。Draw a frosty ice fractal (Cesàro polyline): Koch-like, but the 60° spike becomes an adjustable fold (90° right angle by default) for a frost-like zigzag. Set iterations (1–9) and fold angle (10–170°); export PNG.
流蛇分形（戈斯珀曲线）Draw a Flowsnake Fractal
绘制戈斯珀流蛇曲线：六边形空间填充 L 系统曲线，可调迭代与颜色，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Draw the Gosper flowsnake: a hexagonal space-filling L-system curve. Set iterations and colours; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
皮亚诺分形曲线Draw a Peano Fractal
绘制皮亚诺曲线：经典的空间填充曲线，可调迭代与颜色，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Draw the Peano curve: the classic space-filling curve. Set iterations and colours; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
摩尔分形曲线Draw a Moore Fractal
绘制摩尔曲线：希尔伯特曲线的闭环变体，可调迭代与颜色，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Draw the Moore curve: a closed-loop variant of the Hilbert curve. Set iterations and colours; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
莫顿分形（Z 阶曲线）Draw a Morton Fractal
绘制莫顿 Z 阶曲线：按位交错遍历网格的空间填充折线，可调阶数与颜色，导出 PNG。Draw the Morton Z-order curve: a space-filling polyline from bit-interleaved grid traversal. Set order and colours; export PNG.
V 分形（二叉 V 树）Draw a V-Fractal
绘制二叉 V 分形：从底部一点向上张开一个 V，每条臂的末端再长出缩小到 0.7 倍的同样 V，形成对称的二叉树。可调迭代（1–10）、张角（10–80°）与颜色，导出 PNG。Draw a binary V-fractal: a V opens upward from a base point, and the tip of each arm grows the same V scaled by 0.7, forming a symmetric binary tree. Set iterations (1–10), opening angle (10–80°) and colours; export PNG.
三片雪花分形（谢尔宾斯三角形变体）Draw a Triflake Fractal
绘制三片雪花（triflake，也就是 n=3 的多边形雪花 n-flake）：把等边三角形换成三个边长一半、各占一个角的三角形，中间留出倒三角空洞，反复迭代就得到谢尔宾斯基三角形。可调迭代（1–8）与颜色，导出 PNG。Draw a triflake (the n-flake with n = 3): an equilateral triangle is replaced by three half-size triangles, one in each corner, leaving an upside-down triangular hole in the middle; iterating gives the Sierpiński triangle. Set iterations (1–8) and colours; export PNG.
五片雪花分形Draw a Pentaflake Fractal
绘制五边形雪花（pentaflake）：在大正五边形的五个角上各摆一个更小的五边形，中心再放一个倒置的小五边形，六块互相接触但不重叠，反复迭代。可调迭代（1–5）与颜色，导出 PNG。Draw a pentaflake: a smaller pentagon in each of the five corners of a larger one plus an upside-down one in the centre, all six touching without overlapping, iterated. Set iterations (1–5) and colours; export PNG.
六片雪花分形Draw a Hexaflake Fractal
绘制六边形雪花（hexaflake）：中心与六个角上摆更小的六边形，反复迭代。可调次数与颜色，导出 PNG。Draw a hexaflake: smaller hexagons at the centre and six corners of a larger one, iterated. Set depth and colours; export PNG.
多片雪花分形（任意边数）Draw a Multiflake Fractal
绘制任意边数的多边形雪花（n-flake）：在各顶点方向摆更小的多边形，5 边及以上再在中心放一块；3 边没有中心块，就是谢尔宾斯基三角形，4 边的四块正好拼满。边数 3–12，可调迭代与颜色，导出 PNG。Draw an n-flake: smaller polygons toward each vertex, plus a centre piece from 5 sides up; 3 sides has no centre piece and gives the Sierpiński triangle, and with 4 sides the four pieces fill the square exactly. Sides 3–12; set iterations and colours; export PNG.
图片转拍立得相框Convert Image to Polaroid
把任意图片做成经典拍立得相框：四周加白边，下方留出较宽的空白（可写标题），可调边框厚度、底边高度和背景色。适合纪念照、拼贴和社交媒体配图，支持批量，图片只在浏览器本地处理。Turn any image into a classic Polaroid frame: a white border with a taller blank strip at the bottom for a caption, with adjustable border thickness, bottom height and background colour. Handy for keepsakes, collages and social posts. Works in bulk; images are processed locally in your browser.
创建透明图片（空白 PNG）Create Transparent Image
按指定宽高生成一张完全透明的 PNG（或 WebP）：适合做图层底稿、遮罩模板、透明贴纸底板。可设背景棋盘预览，全部在浏览器本地完成。Create a fully transparent PNG (or WebP) of a chosen width and height - handy as a layer base, mask template or blank sticker sheet. Optional checkerboard preview. Everything runs locally in your browser.
去除图片边框Remove Image Border
自动裁掉图片四周的纯色或透明边框：以左上角颜色（或指定颜色）为边框色，按容差向内裁切；也可按固定像素分别去掉上/右/下/左。会显示每一边去掉了多少。支持批量，图片只在浏览器本地处理。Automatically trim a solid-colour or transparent border from an image. Uses the top-left colour (or a colour you pick) and a tolerance, or removes a fixed number of pixels from top/right/bottom/left. Shows how much was removed on each side. Works in bulk; images are processed locally.
去除图片中的指定颜色（变透明）Remove Specific Color from Image
把图片中指定颜色变成透明：可点预览取色，设容差和边缘柔化，适合抠白底、绿幕或去掉单一色块。显示修改了多少像素，支持批量，图片只在浏览器本地处理。Make a chosen colour in an image transparent. Click the preview to pick the colour, set a tolerance and edge softness - handy for white backgrounds, green screens or removing a flat colour block. Shows how many pixels changed. Works in bulk; images are processed locally.
显示图片的 YCbCr 颜色通道Show YCbCr Image Colors
把图片拆成 Y（亮度）、Cb、Cr（色度）三个通道分别预览：可选显示单通道灰度图，或把 Cb/Cr 映射成假彩色，便于理解 JPEG/视频压缩里的颜色空间。支持批量，图片只在浏览器本地处理。Split an image into Y (luma), Cb and Cr (chroma) channel previews - as greyscale planes or false-colour Cb/Cr maps - to see how JPEG and video colour spaces work. Works in bulk; images are processed locally.
整数列表转图片Create Image from Integers
把整数列表画成图片：按灰度（0–255）或 RGB 三元组填充像素，可指定宽度。适合把数据矩阵可视化，本地处理。Paint a list of integers as an image: greyscale values (0-255) or RGB triples, with a chosen width. Handy for visualizing data matrices. Processed locally.
生成康托尔集（梳状图）Generate Cantor Set
生成康托尔集的梳状可视化：每一步去掉线段中间三分之一，逐行展示。可导出 PNG，本地完成。Generate a Cantor-set comb: remove the middle third of each segment at every step, shown row by row. Export PNG locally.
生成非对称康托尔集Generate Asymmetric Cantor Set
生成非对称康托尔梳：每步按可调左右比例去掉中间一段，而不是固定的三等分。导出 PNG，本地完成。Generate an asymmetric Cantor comb: remove a middle gap with adjustable left/right keep ratios instead of equal thirds. Export PNG locally.
生成康托尔尘Generate Cantor Dust
生成二维康托尔尘：把正方形分成 3×3 格，只保留四个角，再对每个角反复同样操作，形成粉尘状点集。导出 PNG。Generate 2D Cantor dust: split a square into 3×3 cells, keep only the four corners, and repeat on each corner to get a dust of points. Export PNG.
生成切萨罗分形Generate Cesàro Fractal
生成切萨罗分形（类科赫曲线，转折角约 85°），可调迭代次数，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Cesàro fractal (Koch-like with ~85° turns). Set iterations; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成切萨罗多边雪花Generate Cesàro Polyflake
在正多边形边上绘制切萨罗型折线，形成多边雪花。可调边数与迭代，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Draw Cesàro-style polylines on a regular polygon to form a polyflake. Set sides and iterations; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成龙曲线Generate Dragon Curve
生成贺氏龙曲线（Heighway dragon）：用 L 系统迭代折线，可调次数与颜色，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Heighway dragon curve via an L-system. Set iterations and colours; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成斐波那契词分形Generate Fibonacci Word Fractal
根据斐波那契词画折线分形：读 0 右转 90°，读 1 左转 90°，每步前进。可调次数，导出 PNG。Draw a fractal polyline from the Fibonacci word: turn right 90° on 0, left 90° on 1, stepping forward each time. Set depth; export PNG.
生成广义康托尔集Generate Generalized Cantor Set
生成广义康托尔梳：每步按可调保留比例去掉中间空隙（左右对称）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a generalized Cantor comb with an adjustable keep ratio (symmetric). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成戈斯珀曲线Generate Gosper Curve
生成戈斯珀流蛇曲线。可调迭代，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Gosper flowsnake. Set iterations; export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成 H 分形（H 树）Generate H Fractal
生成 H 树分形。可调迭代，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「层数」。Generate an H-tree fractal. Set iterations; export PNG. Settings: Width, Height, Padding, Line width, Levels.
生成海威三角龙Generate Heighway Triangle
生成三角版龙曲线（120°）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a triangular dragon curve (120°). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成六角龙曲线Generate Hexadragon Curve
生成六角龙（60° 龙曲线）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a hexadragon (60° dragon). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成希尔伯特曲线Generate Hilbert Curve
生成希尔伯特空间填充曲线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Hilbert space-filling curve. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成科赫反雪花Generate Koch Anti-snowflake
生成科赫反雪花（内凹）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Koch anti-snowflake (inward). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成科赫多边雪花Generate Koch Polyflake
在正多边形边上绘制科赫折线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Draw Koch polylines on a regular polygon. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成科赫雪花Generate Koch Snowflake
生成经典科赫雪花。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the classic Koch snowflake. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成科赫三角分形Generate Koch Triangle Fractal
生成单条科赫折线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a single Koch polyline. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成莱维 C 曲线Generate Lévy C Curve
生成莱维 C 曲线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Lévy C curve. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成摩尔曲线Generate Moore Curve
生成摩尔曲线（希尔伯特的闭环变体）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Moore curve (closed-loop Hilbert variant). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成皮亚诺曲线Generate Peano Curve
生成皮亚诺空间填充曲线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Peano space-filling curve. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成毕达哥拉斯树Generate Pythagoras Tree
生成毕达哥拉斯树：在正方形顶边上搭一个直角三角形，再在两条直角边上各长出一个较小的正方形，反复迭代。可调分叉角，导出 PNG。Generate a Pythagoras tree: a right triangle sits on the top edge of a square and a smaller square grows on each of its two legs, repeated. Set the branch angle; export PNG.
生成四角龙曲线Generate Quaddragon Curve
生成四角龙（90° 龙的变体走法）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a quaddragon (90° dragon-style variant). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成二次十字分形Generate Quadratic Cross Fractal
生成二次十字分形：十字反复向四臂生长。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a quadratic cross fractal: a cross that grows on all four arms. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成二次科赫岛Generate Quadratic Koch Island
生成二次科赫岛（方版科赫，转角 90°）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a quadratic Koch island (square Koch with 90° turns). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成谢尔宾斯基站箭头曲线Generate Sierpinski Arrowhead Curve
生成谢尔宾斯基箭头曲线（L 系统）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Sierpinski arrowhead curve (L-system). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成谢尔宾斯基地毯Generate Sierpinski Carpet
生成谢尔宾斯基地毯：正方形反复挖去中心九分之一。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「背景」。Generate the Sierpinski carpet by repeatedly removing the centre ninth of each square. Export PNG. Settings: Width, Height, Padding, Iterations, Background.
生成谢尔宾斯基曲线Generate Sierpinski Curve
生成闭合的谢尔宾斯基曲线（正方形版 L 系统）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a closed Sierpinski curve (square L-system). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成谢尔宾斯基六边形Generate Sierpinski Hexagon
生成谢尔宾斯基六边形：把六边形换成六个 1/3 大小、位于各个角上的小六边形（中间留空），反复迭代。导出 PNG。Generate the Sierpinski hexagon: each hexagon is replaced by six copies at 1/3 size placed at its corners, leaving the centre empty, repeated. Export PNG.
生成谢尔宾斯基迷宫Generate Sierpinski Maze
「谢尔宾斯基迷宫」没有独立的标准定义；常说的就是高迭代下的谢尔宾斯基箭头曲线，通道细密，看起来像迷宫。本页画的正是箭头曲线（L 系统 X→YF+XF+Y、Y→XF−YF−X，转角 60°），与「生成谢尔宾斯基箭头曲线」结果相同，完整说明见该工具。导出 PNG。There is no separate standard definition of a "Sierpinski maze"; the name usually refers to the Sierpinski arrowhead curve at high depth, whose narrow corridors look like a maze. This page draws exactly that curve (L-system X→YF+XF+Y, Y→XF−YF−X, 60° turns), the same result as Generate Sierpinski Arrowhead Curve, which has the full explanation. Export PNG.
生成谢尔宾斯基五边形Generate Sierpinski Pentagon
生成五边形谢尔宾斯基分形。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「背景」。Generate a pentagonal Sierpinski fractal. Export PNG. Settings: Width, Height, Padding, Iterations, Background.
生成谢尔宾斯基多边雪花Generate Sierpinski Polyflake
在正多边形顶点上迭代谢尔宾斯基式缩放。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「边数」。Iterate Sierpinski-style scaling on a regular polygon vertices. Export PNG. Settings: Width, Height, Padding, Iterations, Sides.
生成谢尔宾斯基筛（垫片）Generate Sierpinski Sieve
生成谢尔宾斯基三角形垫片（筛）：大三角去掉中心，三角递归。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「背景」。Generate the Sierpinski triangle gasket (sieve): remove the centre triangle recursively. Export PNG. Settings: Width, Height, Padding, Iterations, Background.
生成谢尔宾斯基方块Generate Sierpinski Square
「谢尔宾斯基方块」没有独立的标准定义。本页的规则是：把正方形分成 3×3 九格，只保留四个角，再对每个角重复——这正是康托尔尘（Cantor dust），结果与「生成康托尔尘」相同，完整说明见该工具。去掉中间一格、保留 8 格的版本是谢尔宾斯基地毯。导出 PNG。There is no separate standard definition of a "Sierpinski square". The rule used here, split a square into a 3×3 grid, keep only the four corners and repeat on each, is exactly Cantor dust, the same result as Generate Cantor Dust, which has the full explanation. The version that removes only the centre cell and keeps 8 is the Sierpinski carpet. Export PNG.
生成 Smith–Volterra–Cantor 集Generate Smith–Volterra–Cantor Set
生成 Smith–Volterra–Cantor（肥康托尔）集梳状图：第 n 步从每段中间去掉长 1/4ⁿ（即 1/2²ⁿ）的空隙。第一行是原线段，第 k+1 行是做完 k 步后的结果。导出 PNG。Generate a Smith–Volterra–Cantor (fat Cantor) set as a comb: at step n remove a middle gap of length 1/4ⁿ (that is 1/2²ⁿ) from each interval. The first row is the original segment and row k+1 shows the result after k steps. Export PNG.
生成 T-方块曲线Generate T-Square Curve
生成 T 方块（T-square）分形：从一个实心正方形开始，在它的四个角上各放一个边长一半、中心正好落在角上的实心正方形；之后每一步在最新一批方块露在外面的三个角上继续这样做。导出 PNG。Generate the T-square fractal: start with a filled square and place a filled square of half the side centred on each of its four corners; at every later step do the same on the three outer corners of the newest squares. Export PNG.
生成三龙曲线Generate Terdragon Curve
生成三龙（terdragon）曲线：120° 龙曲线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the terdragon curve: a 120° dragon. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
生成三片雪花曲线Generate Triflake Curve
生成三片科赫雪花拼成的 triflake。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a triflake from three Koch snowflakes. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.