In this talk, we shall explore some of the hyperbolic geometry behind these pictures, which are beautiful examples of mathematical artistry.Īs every calculus student knows, mathematicians spend all day computing integrals. Their fruitful exchange is the basis for four woodcuts which are called Circle Limit I-IV. You can drag and drop layers from this fractal and use them freely in your own work.Abstracts from Previous Pizza Seminars (in reverse chronological order): Spring 2021Įscher's Circle Limit : Exploring hyperbolic tessellationsĮscher was inspired by tessellations of hyperbolic space which Coxeter studied and interpreted them artistically as woodcuts. To use: Highlight and copy the parameters below and paste them into Ultra Fractal. Contact me first if you want to use this for any commercial project other than deviantArt prints. Hit download for the full resolution render at 3600x2400. However, I would like to be credited if you use it. The preview image is also stock and is free for all noncommercial use and deviantArt prints. No credit is required if you use these parameters or layers, but it is nice. It is also free for use in deviantArt prints. Use of this fractal and all layers is completely unrestricted for derivative works for noncommercial use. You can see some of my fractal work on my main account:Īnd finally, the parameters. I use this technique all the time, but it's not always obvious. You can skew the vignette to make an oval or try changing the trap shape and/or aspect ratio in the colouring tab for different vignette shapes.ĭon't be afraid to experiment! I hope some of you will find this tip to be useful. You can move the vignette to focus on different parts of your image. The effect doesn't have to be as obvious as it is here – in some cases using a very low opacity vignette or lighting layer is hardly perceptible but has a huge impact on the final outcome of a piece. The uses for soft masks like this are almost infinite if you play with different shapes and sizes. You can use this same technique to create nice lighting effects if you set the merge mode to screen, soft/hard light or overlay, depending on the gradient you use and the fractal you're working on. Change the gradient to alter the vignette size and how abruptly it fades. Try experimenting with different colours and merge modes. You can combine multiple vignette masks and layers to create many interesting effects in your UF work. Set on multiply, I think it adds a nice dramatic touch and helps draw the viewer in to the focus of the fractal. This is a very useful technique that I use a lot in my own fractal art.ģ.Third layer – this is the actual Vignette Layer. This way, it just adds some nice detail where it's needed and doesn't distract from the main focal point. If you hide the mask you'll see that it would be way too busy in the centre of the fractal without it and in my opinion would completely ruin the image. Not too exciting in itself but you will notice that I've also added a Vignette Mask so the texture is only applied to the edges and fades softly into the centre. A nice mandelbrot zoom that could use a little spicing up.Ģ.Second layer – this is a texture I've made with the Triangle Inequality Average colouring, set to Hard Light. There are three layers and one mask, I'll explain them from the bottom up.ġ.First layer – background fractal. It's a good technique that I use a lot to add drama and interest to my UF work. I've made a simple fractal to illustrate the use of Vignette layers and masks in Ultra Fractal.
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