What makes this a "V-tree" or "Y-tree" specifically?

At every branch point, exactly one parent branch splits into two children, splayed symmetrically apart from the parent's direction, forming a V or Y shape at each junction. That two-way symmetric split, repeated recursively at every child, is what distinguishes this family of fractals from constructions with a different number of children per split.

How much do the branches shrink and spread at each generation?

Each child branch is about 72% the length of its parent, and it's angled about 30 degrees away from the parent's direction, one child turning left, the other turning right. Applied recursively, this steady shrink-and-splay produces the tapering, fanning-out silhouette typical of plant and tree branching models.

What does the Depth setting control?

Depth (0 to 12) sets how many generations of splitting to draw, starting from a single trunk at depth 0. Since every branch spawns exactly 2 children, the total branch segment count is 2^(depth+1) - 1, so depth 12 already produces over 8,000 branch segments.

Is this a real, named fractal construction?

Yes, symmetric binary branching trees like this one are a well-documented family of fractals, often called a fractal canopy or fractal tree, and they're a standard model for the self-similar branching seen in real plants, blood vessels, and river deltas.

V-tree Fractal Generator - Y-Branching Recursive Tree SVG

Overview

Introduction

Plants, blood vessels, and river deltas all share a common branching pattern: a stem splits into two, each of those splits again, and the resulting structure looks strikingly similar whether you zoom in or out. This tool draws that pattern directly.

Choose a depth, and a single trunk recursively splits into two shrinking, splayed-apart branches at every generation, tracing out the classic Y/V-branching tree silhouette.

What Is Generate a V-tree Fractal?

A generator for a symmetric binary branching tree fractal (sometimes called a fractal canopy), built by recursively splitting every branch into exactly two children at a fixed angle and shrink ratio.

There is no text input or output, just a single numeric Depth control; the tool computes every branch's position, angle, and length internally and renders the result as SVG line segments.

How Generate a V-tree Fractal Works

The trunk starts at a fixed point, pointing straight up, with a starting length. At every branch point, two child branches are drawn, one rotated about 30 degrees clockwise from the parent's direction, the other rotated about 30 degrees counter-clockwise, both starting from the parent branch's endpoint.

Each child branch's length is about 72% of its parent's length, so branches steadily taper as the generations progress, mimicking how real plant branches narrow toward their tips.

This split-shrink-and-splay step repeats recursively at every new branch until the chosen depth is reached, so the total branch count doubles with every generation while each generation's branches get shorter and spread further apart from the trunk's original direction.

When To Use Generate a V-tree Fractal

Use it to demonstrate how a strikingly organic-looking, tree-like structure can emerge from one small, purely deterministic recursive rule, no randomness involved.

It's a useful comparison point against the H-tree Generator and Pythagoras Tree Fractal Generator, since all three build branching structures from different underlying rules, letting you see how the exact split rule shapes the resulting silhouette.

Often used alongside Generate a Pythagoras Tree Fractal and Generate an H-fractal.

Features

Advantages

Produces an immediately recognizable, organic-looking tree silhouette from a fully deterministic recursive rule.
Depth range extends to 12, covering a wide span from a simple single split to a dense, many-branched canopy.
Exports as clean vector SVG or a flattened PNG for use in illustrations, generative-art pieces, or teaching material.

Limitations

The branching angle (about 30 degrees) and shrink ratio (about 72%) are fixed internally rather than user-adjustable, only depth is exposed as a control.
Depth is capped at 12 for renderability, since total branch count grows as 2^(depth+1) - 1 and already exceeds 8,000 segments by that depth.

Examples

Depth 0

Input

Depth = 0

Output

A single trunk segment with no branching yet.

At depth 0, the recursive split hasn't been applied, so only the starting trunk is drawn.

Depth 9

Input

Depth = 9

Output

A dense, fanning canopy of branches tapering from a thick trunk down to many thin, splayed-out tips.

Total branch segments follow 2^(depth+1) - 1, so depth 9 produces 1,023 segments across all generations.

Best Practices & Notes

Best Practices

Start around depth 6 to 9 to see the full recognizable canopy shape clearly before pushing toward the depth-12 maximum, where the finest branches become very short.
Compare it against the H-fractal Generator at a similar depth to see how a fixed 90-degree, 4-way split produces a very different silhouette from this 2-way, 30-degree split.

Developer Notes

Implemented as a recursive `branch` function that, given a starting point, heading, and length, draws one segment forward then recurses into two children at `heading + spread` and `heading - spread` with `length * shrink`, using a fixed `spread` of PI/6 (30 degrees) and `shrink` of 0.72. Geometry is normalized into the shared 1000x1000 SVG viewBox afterward.

Generate a V-tree Fractal Use Cases

Illustrating how deterministic recursive branching produces organic, plant-like silhouettes without any randomness
Comparing different branching-fractal rules (2-way splayed split versus the H-tree's 4-way right-angle split, or the Pythagoras tree's square-based split)
Generating a tree-like SVG illustration for a nature-themed page, article, or generative-art piece

Common Mistakes

Expecting a randomized, unique-looking tree on every generation, this construction is fully deterministic, the same depth always produces the exact same branch layout.
Confusing it with the Random Tree Generator elsewhere on the site, that tool adds randomized angle jitter and leaf coloring; this one uses a fixed, repeatable split rule with no randomness.

Tips

Try the Pythagoras Tree Fractal Generator next to see a branching structure built from squares and right triangles instead of simple line segments.
Download as SVG if you want to recolor or thicken specific branch generations afterward in a vector editor.

Generate a V-tree Fractal