Because of the self-similarity properties of nature, fractals are widely adopted as generators of natural object multimedia contents. Unfortunately, fractals are difficult to control due to their iterated function systems, and traditional researches on fractal generating visual objects focus on mathematical manipulations. In Generative Adversarial Nets (GANs), visual object generators can be automatically guided by a single image. In this work, we explore the problem of guiding fractal generators with GAN. We assume that the same category of fractal patterns is produced by a group of parameters of initial patterns, affine transformations and random noises. Connections between these fractal parameters and visual objects are modeled by a Gaussian mixture model (GMM). Generator trainings are performed as gradients on GMM instead of fractals, so that evaluation numbers of iterated function systems are minimized. The proposed model requires no mathematical expertise from the user because parameters are trained by automatic procedures of GMM and GAN. Experiments include one 2D demonstration and three 3D real-world applications, where high-resolution visual objects are generated, and a user study shows the effectiveness of artificial intelligence guidances on fractals.

中文翻译：

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具有对抗学习的高斯混合噪声随机分形用于自动创建视觉对象

由于自然的自相似性，分形被广泛用作自然对象多媒体内容的生成器。不幸的是，分形因其迭代的函数系统而难以控制，传统的分形生成视觉对象的研究集中在数学操作上。在生成对抗网络 (GAN) 中，视觉对象生成器可以由单个图像自动引导。在这项工作中，我们探讨了用 GAN 引导分形生成器的问题。我们假设相同类别的分形图案是由一组初始图案、仿射变换和随机噪声的参数产生的。这些分形参数和视觉对象之间的连接由高斯混合模型 (GMM) 建模。生成器训练是作为 GMM 上的梯度而不是分形进行的，使得迭代函数系统的评估次数最小化。所提出的模型不需要用户的数学专业知识，因为参数是由 GMM 和 GAN 的自动程序训练的。实验包括一个 2D 演示和三个 3D 真实世界应用程序，其中生成高分辨率视觉对象，并且用户研究显示了人工智能指导对分形的有效性。