geometric shapes

flowerpuppy  asked:

Ur ocs are nice and cute. Could you introduce them? I wanna know more about them.

hey thank you, puppy. im afraid there isn’t much to tell but…

Knut
a young boy who is good at math.
his hair attracts “human tadpoles” and “geometric shapes”.
he seems bored but is not. likes tadpoles.


Nikko
knut’s best friend. a bit narcissistic but tries his best.
he is a wild boy with a big heart and good looks.
his outfit is a pajama.


Gacha-BURUMA
a perv boy with a low self-esteem. needs to wear glasses but is embarrassed.
adores school (never went there).


Eme
gets motion sickness from walking. always cold and in bed or warm bath.
a really sensitive boy. lives in a cottage and believes in bunny angels.
don’t make him cry.

Choose A Mandala & Discover What It Reveals About You

Okay, I want you to do a little exercise with me. Close your eyes, take a deep breath 3 times. Open your eyes and look over the graphic below. Choose which mandala speaks to you personally. Which one are you drawn to?


Now scroll down, find it and find out what it means…


anonymous asked:

Hello friend! Although I've been practicing in digital art for almost 3 years, I'm never completely satisfied by the result of my works. I usually never like the coloring. And from what I've seen you have the most unique and beautiful coloring style. So, I wanted to ask you, how did you find it? How did you expirement and settled in this style? Thank you for your time!

!!!! Thank you so much! ;v; 

We’ll start with ygo !!  because everything else before that is Dark Past and absolutely terrifying Never Again

early 2015, I used to try doing semirealistic art because artists like jiyu-kaze, artgerm, and sakimichan
the last piece took probably 2 weeks???? it was painful lmao

I used to do the thing where you painted everything in grayscale first and then used a bunch of layer modes to layer colors on top, inspired by this, and it carried over to my tg art. it would take maybe long time to finish anything because I didn’t really know how to use it correctly. 

 Then my style started off being inspired by sui-zakki  (the author of tg), especially these pieces xx, x

I switched to using base colors after a while and tried to paint the way ishida did. I really liked the way that his art wasn’t exactly smooth?? or that you could still see the edges of each color next to each other… the colors looked really sharp and abstract. You could say this is the start of the style I have right now <:
Along with base colors, I used a lot of lumi & shade layers to add highlights and shadows. My backgrounds were usually a lot softer and sort of random at the time (I think you can see my style improvement best through the way I drew/colored my backgrounds ‘v’ )

Around 2016ish, the colors I used were lighter because I used less lumi & shade and used more on overlay and multiply layers (this is what I do now) or by coloring with only changes in opacity (this was mostly influenced by ammeja). There’s the prominent geometric edges or whatever in my colors because I started using a more square-ish brush for everything and I really liked how it looked when the colors weren’t seamlessly blended together. (the victor in the center was my first yoi fan art, he looks so different now asjdfjgjgjgjf :’> )

I color in a more blocky/geometric style, and instead of painting my pieces and smoothing them out like the ones above, I just stuck with sketches/lineart (this old tg piece is the one that got me to stick to lineart).
My coloring was mainly influenced by barachan, lanxin, and seventypercentethanol, and their pieces like xx, x
yahoberries (I love her art so much you don’t understand) influenced my blue/white outlines as well as the stray blob of colors that I sometimes don’t erase around my art
I really like crystal/gem-looking colors, and having geometric shapes as highlights or shades looked pretty cool too, so that’s how my style happened <3

Regarding Fractals and Non-Integral Dimensionality

Alright, I know it’s past midnight (at least it is where I am), but let’s talk about fractal geometry.

Fractals

If you don’t know what fractals are, they’re essentially just any shape that gets rougher (or has more detail) as you zoom in, rather than getting smoother. Non-fractals include easy geometric shapes like squares, circles, and triangles, while fractals include more complex or natural shapes like the coast of Great Britain, Sierpinski’s Triangle, or a Koch Snowflake.

Fractals, in turn, can be broken down further. Some fractals are the product of an iterative process and repeat smaller versions of themselves throughout them. Others are more natural and just happen to be more jagged.

Fractals and Non-Integral Dimensionality

Now that we’ve gotten the actual explanation of what fractals are out of the way, let’s talk about their most interesting property: non-integral dimensionality. The idea that fractals do not actually have an integral dimension was originally thought up by this guy, Benoit Mandelbrot.

He studied fractals a lot, even finding one of his own: the Mandelbrot Set. The important thing about this guy is that he realized that fractals are interesting when it comes to defining their dimension. Most regular shapes can have their dimension found easily: lines with their finite length but no width or height; squares with their finite length and width but no height; and cubes with their finite length, width, and height. Take note that each dimension has its own measure. The deal with many fractals is that they can’t be measured very easily at all using these terms. Take Sierpinski’s triangle as an example.

Is this shape one- or two-dimensional? Many would say two-dimensional from first glance, but the same shape can be created using a line rather than a triangle.

So now it seems a bit more tricky. Is it one-dimensional since it can be made out of a line, or is it two-dimensional since it can be made out of a triangle? The answer is neither. The problem is that, if we were to treat it like a two-dimensional object, the measure of its dimension (area) would be zero. This is because we’ve technically taken away all of its area by taking out smaller and smaller triangles in every available space. On the other hand, if we were to treat it like a one-dimensional object, the measure of its dimension (length) would be infinity. This is because the line keeps getting longer and longer to stretch around each and every hole, of which there are an infinite number. So now we run into a problem: if it’s neither one- nor two-dimensional, then what is its dimensionality? To find out, we can use non-fractals

Measuring Integral Dimensions and Applying to Fractals

Let’s start with a one-dimensional line. The measure for a one-dimensional object is length. If we were to scale the line down by one-half, what is the fraction of the new length compared to the original length?

The new length of each line is one-half the original length.

Now let’s try the same thing for squares. The measure for a two-dimensional object is area. If we were to scale down a square by one-half (that is to say, if we were to divide the square’s length in half and divide its width in half), what is the fraction of the new area compared to the original area?

The new area of each square is one-quarter the original area.

If we were to try the same with cubes, the volume of each new cube would be one-eighth the original volume of a cube. These fractions provide us with a pattern we can work with.

In one dimension, the new length (one-half) is equal to the scaling factor (one-half) put to the first power (given by it being one-dimensional).

In two dimensions, the new area (one-quarter) is equal to the scaling factor (one-half) put to the second power (given by it being two-dimensional).

In three dimensions, the same pattern follows suit, in which the new volume (one-eighth) is equivalent to the scaling factor (one-half) put to the third power.

We can infer from this trend that the dimension of an object could be (not is) defined as the exponent fixed to the scaling factor of an object that determines the new measure of the object. To put it in mathematical terms:

Examples of this equation would include the one-dimensional line, the two-dimensional square, and the three-dimensional cube:

½ = ½^1

¼ = ½^2

1/8 = ½^3

Now this equation can be used to define the dimensionality of a given fractal. Let’s try Sierpinski’s Triangle again.

Here we can see that the triangle as a whole is made from three smaller versions of itself, each of which is scaled down by half of the original (this is proven by each side of the smaller triangles being half the length of the side of the whole triangle). So now we can just plug in the numbers to our equation and leave the dimension slot blank.

1/3 = ½^D

To solve for D, we need to know what power ½ must be put to in order to get 1/3. To do this, we can use logarithms (quick note: in this case, we can replace ½ with 2 and 1/3 with 3).

log_2(3) = roughly 1.585

So we can conclude that Sierpinski’s triangle is 1.585-dimensional. Now we can repeat this process with many other fractals. For example, this Sierpinski-esque square:

It’s made up of eight smaller versions of itself, each of which is scaled down by one-third. Plugging this into the equation, we get

1/8 = 1/3^D

log_3(8) = roughly 1.893

So we can conclude that this square fractal is 1.893-dimensional.

We can do this on this cubic version of it, too:

This cube is made up of 20 smaller versions of itself, each of which is scaled down by 1/3.

1/20 = 1/3^D

log_3(20) = roughly 2.727

So we can conclude that this fractal is 2.727-dimensional.

2

Today’s gonna be a bit different. That’s because I did this job at the beginning of the week! Actually, this is part 1 of 3 arts I did at this client’s house.

For this one, I designed a geometric pattern with pastel colors combination to fill this living room wall and give it a touch of movement with some modern shape. I really liked the final result.

In the next week I’ll be posting the other 2 arts I did there. Hope you enjoy it. And if you want to see more photos and videos from this wall process, just head over @sketchdequinta on Instagram. :)