Here's an execution for 2, 3. When Furthermore, note that if therefore we can always make
a != 1 we use a as the extra numbers instead of b: 1 | 2 2(1) ...
2 | 2 2(0) 2(1) ...
3 | 3 2(1) 2(0) 2(1) ...
4 | 3 2(0) 2(0) 2(1) ...
5 | 2 3(2) 2(1) 2(0) 2(0) ...
6 | 2 3(1) 2(1) 2(0) 2(1) ...
7 | 2 3(0) 2(1) 2(0) 2(1) ...
8 | 3 3(2) 2(0) 2(0) 2(1) ...
9 | 3 3(1) 2(0) 2(0) 2(1) ...
10 | 3 3(0) 2(0) 2(0) 2(1) ...
11 | 2 2(1) 3(2) 2(1) 2(0) 2(1) ...
12 | 2 2(0) 3(2) 2(1) 2(0) 2(1) ...
13 | 3 2(1) 3(1) 2(1) 2(0) 2(1) ...
14 | 3 2(0) 3(1) 2(1) 2(0) 2(1) ...
15 | 2 2(1) 3(0) 2(1) 2(0) 2(1) ...
16 | 2 2(0) 3(0) 2(1) 2(0) 2(1) ...
17 | 3 3(2) 3(2) 2(0) 2(0) 2(1) ...a = 1, then the a, b sequence is a subset of the b, a sequence e.g.:1, 2 = [1, 2, 2, 1, 1, 2, 1, ...]
2, 1 = [ 2, 2, 1, 1, 2, 1, ...]a not be 1 by switching the pair and then using the generalized algorithm with a != 1.This algorithm is more efficient in space, using only , as it recursively compresses the state required to keep track of what to do next.
Time is still .
The table at maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf page 20 has a summary image, but it is hard to understand.
1 2(0) 1(1)The starting state is:which means that it implicitly contains infinitely many The actual algorithm will of course omit as many trailing
2 | 2 2(1) 2(1) 2(1) 2(1) ...2(1) at the end which we abbreviate just as:2 | 2 2(1) ...2(1) as it can.The update rules are:Note that both rules don't overlap so that each update is always determined by only one of them at a time.
- go left to right:
- flip:continue going left to right.
x(0) y(0) !x((!x)-1) unchanged - repeat:and then stop further updates.
x(0) y(n > 0) x(x-1) y(n - 1)
- flip:
Also the first column is always implicitly
(0).2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...Here we:
2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...
5 | 1 2(0) 2(1) 2(0) 2(1) ... 2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...
5 | 1 2(0) 2(0) 2(1) ...
6 | 2 1(0) 2(1) 2(0) 2(1) ...
7 | 1 1(0) 2(0) 2(0) 2(1) ...
8 | 2 2(1) 1(0) 2(1) 2(0) 2(1) ...
9 | 2 2(0) 1(0) 2(1) 2(0) 2(1) ...
10 | 1 1(0) 1(0) 2(0) 2(0) 2(1) ...
11 | 2 2(1) 2(1) 1(0) 2(1) 2(0) 2(1) ...
12 | 2 2(0) 2(1) 1(0) 2(1) 2(0) 2(1) ...
13 | 1 2(1) 2(0) 1(0) 2(1) 2(0) 2(1) ...
14 | 1 2(0) 2(0) 1(0) 2(1) 2(0) 2(1) ...
15 | 2 1(0) 1(0) 1(0) 2(0) 2(0) 2(1) ...
16 | 1 2(1) 2(1) 2(1) 1(0) 2(1) 2(0) 2(1) ...The generalized Kolakoski sequence is the generalization of the Kolakoski sequence where you don't need to restrict yourself to 1,2 but can instead use any a,b pair.
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If you are exploring the world of mixed media art in Australia, selecting the right canvas can make a big difference. Artists often face challenges in choosing the right surface to support various materials such as acrylic, oil, watercolor, pastels, and collage. Using specialty canvas ensures your artwork lasts longer, holds texture well, and offers vibrant results. In this guide, we’ll explore the top 4 specialty canvas types for mixed media in Australia, highlighting their unique benefits and ideal uses.
Cotton canvas is one of the most popular options for mixed media artists in Australia. It is flexible, affordable, and readily available. The natural cotton fibers provide excellent texture, allowing paints and mediums to adhere well. Cotton canvases come in various weights, usually ranging from 10 to 20 ounces per square yard, giving artists freedom to choose based on their techniques.
Many artists appreciate cotton canvas for its absorbency. It works well with acrylic paints, charcoal, and pastels. This canvas type is also perfect for layering techniques, as the fibers handle repeated applications without losing strength. You can experiment with washes and glazes, achieving a professional look for your mixed media art.
Additionally, cotton canvas is versatile for framing or stretching. Many Australian art stores stock pre-stretched cotton canvases in standard and custom sizes. www.canvasprintsaustralia.net.au/ offers best quality canvas print australia, making it convenient for artists seeking high-quality materials for their projects.
2. Linen Canvas for Professional Finish
Linen canvas is considered a premium choice for mixed media enthusiasts. It is stronger than cotton and has a finer, smoother surface, which helps in achieving precise details. Linen naturally resists warping and can last for decades, making it a reliable choice for artwork meant for exhibitions or gallery sales.
The texture of linen canvas enhances brushwork and holds pigments exceptionally well. Acrylics, oils, and ink layers adhere beautifully, creating depth and richness. Artists often notice that colors appear brighter and more vibrant on linen, giving the final piece a sophisticated finish.
Despite its higher cost, linen canvas is worth considering for serious projects. It is lightweight yet sturdy, ideal for large-scale works. Many Australian artists prefer linen for creating wall art that combines multiple media, including pencil sketches, pastels, and collage elements.
3. Watercolor Canvas for Fluid Techniques
Watercolor canvas is specially designed to mimic traditional watercolor paper. Unlike standard canvases, this type is treated to hold water-based media without buckling or warping. It is perfect for artists who blend watercolor techniques with acrylics or ink washes.
This canvas type allows for smooth washes and gradients. Artists can experiment with splattering, layering, and even wet-on-wet techniques without damaging the surface. The canvas absorbs water evenly, which prevents puddles or uneven drying. It also works well for mixed media projects that include pen, pencil, or gouache details.
In Australia, watercolor canvas is increasingly popular among mixed media artists seeking versatility. It comes in sheets or pre-stretched options suitable for gallery framing. The durability and texture make it a practical choice for creating vibrant wall art or unique canvas art collections.
Primed canvas boards are rigid panels coated with gesso or acrylic primer. They offer a smooth and stable surface for mixed media techniques. Unlike stretched canvases, boards are lightweight, portable, and easier to store. Artists often choose them for experimental projects or when working outdoors.
These boards handle various media types effectively. Acrylic, ink, watercolor, and even collage materials adhere securely without warping. Primed surfaces also allow for repeated layering, making them ideal for textured and dimensional artwork. The smooth finish helps create sharp lines and clean edges, perfect for detailed mixed media projects.
Canvas boards are widely used in Australia for creating small-scale wall art. Their rigidity ensures that even heavy mixed media elements, such as paper or fabric, stay in place. Many artists start with canvas boards to test new techniques before committing to larger stretched canvases.
How to Choose the Right Canvas for Mixed Media
Choosing the right canvas depends on your artistic style, media preferences, and project goals. Consider these factors when making your selection:
Texture: Coarse textures hold thick paints and pastes well, while smooth surfaces are better for detailed work.
Durability: Linen and heavyweight cotton are best for long-lasting pieces.
Absorbency: Watercolor and primed boards absorb water-based paints effectively.
Size and Format: Pre-stretched canvases offer convenience, while boards provide portability.
Experimenting with different canvas types can also help you find your preferred surface. Many Australian art stores offer sample packs for artists to test textures and primers before investing in larger canvases.
Common Questions About Mixed Media Canvases
What is the most versatile canvas for mixed media?
Cotton canvas is generally considered the most versatile option. It supports acrylic, oil, watercolor, and other media while remaining affordable.
Cotton canvas is generally considered the most versatile option. It supports acrylic, oil, watercolor, and other media while remaining affordable.
Can I use watercolor canvas with acrylic paints?
Yes, watercolor canvas works with acrylic paints, but it may require a primer to enhance adhesion.
Yes, watercolor canvas works with acrylic paints, but it may require a primer to enhance adhesion.
Are canvas boards better for travel or outdoor painting?
Yes, their rigidity and lightweight nature make them ideal for portable projects.
Yes, their rigidity and lightweight nature make them ideal for portable projects.
How do I maintain mixed media art on canvas?
Use a protective varnish or fixative to preserve colors and prevent dust accumulation.
Use a protective varnish or fixative to preserve colors and prevent dust accumulation.
Why Australian Artists Prefer Specialty Canvases
Australian artists often face environmental factors such as humidity and sunlight. Specialty canvases like linen and primed boards help maintain artwork integrity under these conditions. Using high-quality canvas also improves pigment adhesion, allowing mixed media projects to retain vibrancy for years.
Moreover, the local art market in Australia values originality and craftsmanship. Investing in the right canvas ensures that artists can create professional-grade wall art that appeals to collectors and galleries. Specialty canvas types provide flexibility for experimentation while supporting long-term durability.
Integrating Canvas into Home and Gallery Spaces
Mixed media canvas art is not limited to studio walls. It can enhance living spaces, offices, or galleries. Choosing the right canvas affects both aesthetic appeal and longevity. For example, a linen canvas with layered acrylics and textures can become a striking focal point in a living room.
Similarly, watercolor canvas pieces often provide soft, ethereal effects, perfect for modern interiors. Primed canvas boards can be framed individually or grouped for gallery-style displays. Using these specialty canvases, artists can adapt their creations to different environments while maintaining artistic integrity.
Tips for Working With Mixed Media Canvases
Rotate your canvas to avoid uneven drying or sagging.
Consider archival-quality canvases for long-term projects.
Following these tips ensures your artwork remains vibrant, textured, and durable. Experimenting with different media combinations also encourages creativity and personal style development.
Conclusion
Selecting the right canvas is crucial for any mixed media artist in Australia. Cotton canvas offers versatility, linen provides a professional finish, watercolor canvas supports fluid techniques, and primed boards offer portability and stability. Understanding the benefits of each type allows artists to choose surfaces that suit their creative goals.
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Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact