Skip to content
A Swift playground that generates beautiful Julia set fractal images.
Swift
Branch: master
Clone or download
gongzhang Merge pull request #2 from reedand/master
Updated to use Substring as 'characters' is deprecated
Latest commit 10fd48b Feb 22, 2018
Permalink
Type Name Latest commit message Commit time
Failed to load latest commit information.
Images
JuliaSet.playground Updated to use Substring as 'characters' is deprecated Feb 12, 2018
.gitignore
LICENSE Initial commit Jul 19, 2016
README.md

README.md

>>> Jump to English Version <<<

朱利亚集合 Playground

此项目是一个能够生成“朱利亚集合(Julia Set) 分形图像的 Swift Playground 工程。朱利亚集合 是分形理论中的经典概念,它可以生成令人惊叹的分形图像。

朱利亚集合 的数学公式简单而优雅:

z(n+1) = z(n)^2 + c

...但它却能够产生出多样的、蕴含无线细节的美丽分形图像:

Xcode 8.3 Playground 截图

想要了解关于 朱利亚集合 的更多知识,请参阅 维基百科 Julia Set 中文条目

关于此项目

我曾与江苏卫视 最强大脑(第四季)节目组合作,共同打造了一个以分形数学为主题的挑战题目。节目现场使用了本项目的提供的分形图生成技术。该期节目于 2017 年 2 月 10 日播出,可以在爱奇艺网站观看:http://www.iqiyi.com/v_19rrapeyvc.html

江苏卫视「最强大脑」第四季,第 2017-2-10 期节目

此项目的核心技术也在我的个人 iOS 应用“分形的奥秘(Mysteries of Fractal) 中使用。强烈推荐给各位,可以在 App Store 中免费下载这个应用:App Store 链接

如何使用代码

下载 JuliaSet.playground 并使用最新版本的 Xcode 就可以编译运行。全部代码文件位于 JuliaSet.playground/Sources 目录下。

如果你有 iPad ,也可以在苹果的 Swift Playgrounds 应用中编译和运行本项目。

API 使用样例

你可以手动指定参数并观察它们如何影响分形图的生成:

let imageSize = CGSize(width: 600, height: 440)
var julia = JuliaSet()

julia.window = 4.0
julia.const = Complex(-0.5, 0.0)
julia.color = JuliaSetColor(
    hue: 0,
    brightness: 0.87,
    saturation: 0.9
)

let outputImage = JuliaSetRenderer.syncRender(julia, pixelSize: imageSize)

你也可以从 分形的奥秘 应用中导出某个特定的分形图,然后将它的代号放在 Playground 中绘制:

var code = "juliaset://?code=25477FFF7FFF7FEB5A4400FE"  // 从“分形的奥秘”中导出的一个分形
let outputImage = JuliaSetRenderer.syncRender(JuliaSet.decodeURL(code)!, pixelSize: imageSize)

渲染程序也支持异步渲染方法,它不会阻塞主线程。如果你准备在实际 iOS 项目中渲染分形图,这个方法就会很有用。

// 在后台渲染...
JuliaSetRenderer.asyncRender(julia, sizeInPixel: imageSize) { outputImage in
    // ...然后在主线程中获取结果
}

更多有趣的数学项目

联系方式


以下为英文版本 README

Julia Set Playground

This repo contains a Swift Playground that generates Julia set fractal images. Julia set is a classical concept in fractal mathematics, and it can be used to generate amazing fractal images.

The formula of Julia set is simple and elegant:

z(n+1) = z(n)^2 + c

...But it can generates varies beautiful fractal images with infinity details:

Xcode 8.3 Playground Screenshot

For more information about Julia set, See https://en.wikipedia.org/wiki/Julia_set.

This project is used in my iOS app Mysteries of Fractal (分形的奥秘). You can download it in the App Store for free. App Store Link

Installation

Just download JuliaSet.playground and open it by latest version of Xcode. All the code is in JuliaSet.playground/Sources folder.

If you have an iPad, you can also run this project using Apple's Swift Playgrounds app.

Sample Code

You can manually adjust the parameters and see how they affect the image:

let imageSize = CGSize(width: 600, height: 440)
var julia = JuliaSet()

julia.window = 4.0
julia.const = Complex(-0.5, 0.0)
julia.color = JuliaSetColor(
    hue: 0,
    brightness: 0.87,
    saturation: 0.9
)

let outputImage = JuliaSetRenderer.syncRender(julia, pixelSize: imageSize)

You can also export a specific fractal from the Mysteries of Fractal app, then draw it in playground:

var code = "juliaset://?code=25477FFF7FFF7FEB5A4400FE"  // exported by "Mysteries of Fractal" app
let outputImage = JuliaSetRenderer.syncRender(JuliaSet.decodeURL(code)!, pixelSize: imageSize)

The render also provides an asynchronous method to generate fractal image, which does not block the main thread. It's useful when you generate big image in a real iOS app.

// render in background...
JuliaSetRenderer.asyncRender(julia, sizeInPixel: imageSize) { outputImage in
    // ...then get result in main thread
}

More Mathematics Playground Projects

Contact

Feel free to contact me if you need more information ;)

Email: gong@me.com

You can’t perform that action at this time.