**These Doodle Insights are brought to you by my super generous supporters on Patreon!**

*How about learning how to render a really cool effect with just a few fairly simple lines of code? Does that sound good?*

**The Twisting Four-Sided Column Effect** is, I assume, a classic * demo-scene* thing because I’ve seen it done on several platforms and by multiple people, including on the Pico-8. I’m pretty sure this effect has an actual name but I have no idea what that would be so I’m just going to call it The Twisting Four-Sided Column Effect.

**Here’s what it looks like!**

**The code for this effect is no more than 25 lines long**, and I’m talking clear code and pretty short lines.

We’re going to get there * step-by-step*, so that at the end

**you’ll be able to make your own version of this effect, hopefully with your own clever**

*twist*!Let’s start with **the four-sided pillar!**

function _draw() cls() local a=time()*0.2 for i=0,0.75,0.25 do local x1=64+32*cos(a+i) local x2=64+32*cos(a+i+0.25) if x1>x2 then rectfill(x1,0,x2,127,7) rect(x1,0,x1,127,0) rect(x2,0,x2,127,0) end end end

What this code does is that **at every frame, we’re drawing the visible sides of the rotating pillars.** *(and their vertical borders)*

First we clear the screen. Then we find a value for ‘a’, **the rotation angle of the pillar.**

Now we’re at the most important part of this effect, **the 4-sides ‘for’ loop**. With ‘i’ going from 0 to 0.75, by 0.25 at a time, **‘i’ will be the normal angle for each of the 4 corners of the pillar**.*(imagine it from above) For each of the corner, the next corner will have the normal ‘i+0.25’*. From there we can have the two

**x coordinates**delimiting each side of the pillar with

**these two lines:**

local x1=64+32*cos(a+i) local x2=64+32*cos(a+i+0.25)

*On the Pico-8, the resolution is 128×128, that’s why we’re using 64 as the ‘center’ value and 32 as ‘width’ value. (mathematically speaking it is not really the width of the pillar but more of a factor – the actual width of the pillar would be 32/√2 – hopefully you get what I mean)*

*Second note: on Pico-8, angles go from 0 to 1 instead of 0-2PI. I wrote another Doodle Insights about this! So 0.25 is the equivalent of 90 degrees or PI/2 radians.*

We have our two x coordinates, **now we need to know whether this side of the pillar should be visible or hidden** behind the other half of the pillar. Nothing easier, all we have to do is * check if x1 comes before or after x2*! If x1 comes before, we’re on

**side A**, if x2 comes before, we’re on

**side B**. It’s up to you to choose which side you make visible, it will not affect the effect whatsoever.

**I’m going with side B here with ‘if x1>x2’.**Now that we know we’re drawing this side, **let’s draw this side!** We have our two x coordinates, so all we have to do is draw **a big rectangle going from x1 to x2** and that takes all the height of the screen. But since we’re not playing with colors yet, **we’re also drawing the limits of each sides** with two black rect calls, to differentiate the white sides.

**We have our pillar! Let’s twist it!**

function _draw() cls() local t=time()/2 for y=0,127 do local yy=y/1024 local a=cos(0.2*sin(t*0.1+yy*2))+0.5*cos(-0.2*t+yy/2) for i=0,0.75,0.25 do local x1=64+32*cos(a+i) local x2=64+32*cos(a+i+0.25) if x1>x2 then rect(x1,y,x2,y,7) pset(x1,y,0) pset(x2,y,0) end end end end

*We have a bigger loop!* **Now we’re processing every horizontal line one by one!** You’ll note that **our rectfill call was traded for a rect call**, *(not that it really matters, rectfill would still work)* as we are only drawing horizontal lines, and the old rect calls, for the limits of each side of the pillar, were traded for pset calls.

Other change: **we have two new values, ‘t’ and ‘yy’.** ‘t’ is just **a shortcut value** we’re using to store the time *(divided by two to make the movements slower)* and ‘yy’ is **also a shortcut value** that is simply ‘y’ divided by a big number so that it’s easier to use with angles.

And of course, **the value for ‘a’ changed!** For our previous iteration we only wanted to * rotate* the pillar, so

*‘a=time()*0.2’*was sufficient, but now we want to

*the pillar in crazy ways, and*

**twist**

*what’s crazier than trigonometry mixed with more trigonometry and some arbitrary numbers?**(pure RNG, that’s what would be crazier, but we want our angles to change smoothly from line to line and from frame to frame – the trigonometry functions have this property)*

Ok, **we have out twisting column! Let’s add some colors!**

plt={0,1,2,8,14,15,7} fillp(0b0101010101010101) function _draw() cls() local t=time()/2 for y=0,127 do local yy=y/1024 local a=cos(0.2*sin(t*0.1+yy*2))+0.5*cos(-0.2*t+yy/2) for i=0,0.75,0.25 do local x1=64+32*cos(a+i) local x2=64+32*cos(a+i+0.25) if x1>x2 then local c=(x1-x2)/(1.5*32)*#plt+1 local ca=plt[flr(c)] local cb=plt[min(flr(c+0.5),#plt)] rect(x1,y,x2,y,ca+cb*16) end end end end

*Note: Pico-8 uses an indexed color palette of 16 colors rather than RGB values.*

**Before we get to everything else, let’s quickly talk about that ‘fillp’ function!** This function was added in the 0.1.11 version of Pico-8, which is still quite recent as I write this. It lets your next draw calls *(rect, circfill, pset, etc…)* **draw two colors instead of just one, in a pattern of your composition.** The pattern is passed as parameter to the ‘fillp’ function * as a bitfield* and from there you can use

*‘color1+color2*16’*as color parameter for your draw calls. Here’s the bitfield I’m giving fillp in this example:

0b 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

**And with this bitfield we get vertical stripes!**

There’s big chances I’ll write a Doodle Insights dedicated to ‘fillp’ at some point, because it’s very cool and **I’m sure there’s tons of creative ways to use it!**

*Parenthesis closed!*** Now the line before ‘fillp’!** We’re defining **an array with the colors we want to see on our twisting column!** They are * in order of lightness* and we’ll want the last color

*(7 – white)*to be shown

**when the side of the pillar is aligned with the screen.**

The other thing that changed is after the ‘if x1>x2’, **where we decide what color should be drawn for each horizontal line.**

*Maybe you thought we’d need some clever maths to get a value that corresponds to the inclination of the plane we’re on. Well nope!* All we need is **the difference between x1 and x2!** If they’re far apart * then this side of the column if angled towards the screen*, if they’re close

*. So we want this difference, vaguely normalized*

**then this side of the column is angled towards the side of the screen***(that’s what the division by ‘1.5*32’ is about)*and then

**set to the scale of our color array.**

To make use of our fillp call, **we’re taking two colors from our array**, the first one is the one from the algebra described above, the second one is the same plus ‘0.5’, which means the two colors will be different only if *‘ca%1>0.5’* and **that’s going to give us a very good gradient!** *(if you didn’t understand that last part, just trust me that the result is pretty because of this)*

**We removed the draw calls for the side outlines** because we can make out the sides just from the color difference now!

**Let’s go further!**

function _draw() cls() local t=time()/2 for y=0,127 do local yy=y/1024 local a=cos(0.2*sin(t*0.1+yy*2))+0.5*cos(-0.2*t+yy/2) local w=32+4*(sin(-t+y/128)+0.5*cos(0.5*t-y/64)) local x=64+16*cos(sin(t*0.1+yy*2)) for i=0,0.75,0.25 do local x1=x+w*cos(i+a) local x2=x+w*cos(i+a+0.25) if x1>x2 then local c=(x1-x2)/(1.5*w)*#plt+1 local ca=plt[flr(c)] local cb=plt[min(flr(c+0.5),#plt)] rect(x1,y,x2,y,ca+cb*16) end end end end

*More trigonometric madness!*

**Two new values are being defined just after ‘a’!** For each horizontal line we are taking * a width ‘w’ *and

*, both of which are defined much the same way as ‘a’, with ‘cos’, ‘sin’ and arbitrary values, put in a random order.*

**a horizontal center ‘x’**From there all we have to do is **use these new values!** The main two lines that changed are these:

local x1=64+32*cos(a+i) local x2=64+32*cos(a+i+0.25) --becomes local x1=x+w*cos(i+a) local x2=x+w*cos(i+a+0.25)

**And that’s it!** **We have our crazy Twisting Four-Sided Column effect!**

From there it’s up to you to bring your own magic to the formula! Here’s a simple example where I made it **five-sided instead of four** and then a slightly more complex example where it’s actually **four four-sided columns**!

This last one with the four columns, **I actually reduced its code to 280 characters ***– the size of a tweet –*** for fun!** **Check it out!**

**That’s it for those doodle insights!** If you enjoyed this, maybe check out **the other Doodle Insights**!* I’ve done a really bad job of writing them regularly these last few months but I’m trying to get back on top of it!*

**If you have any remarks or questions,** do let me know in the comments or on Twitter, *I will do my best to reply!*

**And thank you so much to all my Patreon supporters who are making it possible for me to write this and produce free content in general! Here are their names!**

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**Thank you for reading and make plenty of twisting columns!**

TRASEVOL_DOG

Thanks for the great writeup, this is super useful for people experimenting with graphical effects.

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Hello,

I am trying to transcribe these examples in javascript.

I’m stuck on the second one, where we start to twist the column.

local a = cos (0.2 * sin (t * 0.1 + yy * 2)) + 0.5 * cos (-0.2 * t + yy / 2)

I am aware of the different representation of pico8 angles compared to javascript. So, I tried to adapt, but I can not achieve the same result:

var a = Math.cos ((0.2 * 2 * Math.PI) * Math.sin (time * (0.1 * 2 * Math.PI) + yy * 2)) + 0.5 * Math.cos (- (0.2 * 2 * Math.PI) * time + yy / 2);

Could you tell me what I’m doing wrong please? Thank you in advance

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Hi! To achieve the exact same result you’d need this:

var a = (Math.cos (0.2 * Math.sin ((time * 0.1 + yy * 2) * 2 * Math.PI) * 2 * Math.PI)) + 0.5 * Math.cos ((-0.2 * time + yy / 2) * 2 * Math.PI))) * 2 * Math.PI);

If you keep having problems with cos() and sin(), I would recommend making my_cos() and my_sin() functions, which return cos(angle * 2 * Math.PI) and sin(angle * 2 * Math.PI).

But! It actually doesn’t matter! As long as the result is an angle that varies depending on the yy and time variables, I would actually encourage you to get creative with this kind of code!

Sorry for the late answer, I hope it helps!

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Thanks a lot. It really helped !

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Still have some work to do, but it looks more and more like your example 🙂 Thanks again http://doodle.amstratgraph.eu/doodle-04.html

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Hello, your insights were top notch. Are you thinking in adding more content. I hope you do. Cheers.

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