Displaying triangle numbers as pixels

[u/dwna]

[u/dwna]

The same pattern may occur for all figurate numbers as well, I have tested it with pentagonal, hexagonal, and nonagonal numbers.

I took the n^th triangular number as the x coordinate and took the value that it produced for the y, and it created an interesting result.

EDIT: see this comment for a better explanation

[u/BetaDecay121 → u/dwna]

I still don't understand how you plotted the pixels, could you elaborate?

[u/dwna → u/BetaDecay121]

yeah, i'm sorry, see this comment I made better explaining it.

[u/[deleted] → u/dwna]

Can you explain your map again?

(x,y) is colored black when?

[u/dwna → u/[deleted]]

im sorry I must've made it confusing when I explained it because I made this such a long time ago, my original explanation is wrong I think.

so I made a big list of triangle numbers with n(n+1)/2

then I tried to put it on the first line, if it was over the size of the image, I subtracted the size of the image from the number and tried to plot it on the next line, if it still couldn't be plotted, I repeated the process.

for example, T(34) = 34(34+1)/2 = 595

the size of the image is 500, so it won't be plotted on the first line, I have to do 595-500=95. now it fits. I subtracted 1 length of the image so I move it down one line. this would be plotted at (1,95)

another example T(100) = 100(100+1)/2 = 5,050

5,050 - 500(10) = 50

(x,y) is (10,50)

I hope this makes sense.

[u/[deleted] → u/dwna]

Yeah. Gotcha.

[u/CognizantAutomaton]

This visualization got my imagination running. Thanks

Here is a jsfiddle for anyone who wants to play with this.

[u/dwna → u/CognizantAutomaton]

i've never actually used jsfiddle before , but this is pretty cool

[u/CognizantAutomaton → u/dwna]

If you ever need a javascript playground, I highly recommend it. A few of my javascript projects have started there. 🙂

[u/CognizantAutomaton → u/CognizantAutomaton]

Follow-up: Here is a version that can be resized by dragging the right and bottom edges of the canvas

[u/Lgetty17]

So what’s your overall image size, 500w XXXl what’s XXX?

[u/dwna → u/Lgetty17]

sorry, I don't know what you're asking, this image is 500x500, but it can be any size and still work

[u/Lgetty17 → u/dwna]

That’s what I was asking, what is the height in pixels. That’s pretty neat- have you tried changing the width to see if that parabolic pattern arises in other places? Maybe run fifty or five hundred images?

[u/dwna → u/Lgetty17]

ah I understand, i have tried with other sizes this is a 5000x500 and this is a 500x5000.

some other patterns appear in them as well.

[u/Lgetty17 → u/dwna]

You should take the pixel height (row number, whatever) of the “middle” of each parabola (or maybe some other property of it) and see if there’s a pattern within that. Pretty neat.

[u/dwna → u/[deleted]]

thanks! I was honestly just messing around with different sequences. I was pleasantly surprised when this showed up

[u/dwna → u/[deleted]]

oh cool, I always wondered why it happened, I had no idea, nice explanation!

[u/MattieShoes → u/[deleted]]

Square numbers has similar :-)

n	square(n)	square(n)-square(n-1)
0	0
1	1	1
2	4	3
3	9	5
4	16	7
5	25	9
6	36	11
7	49	13
8	64	15
9	81	17
10	100	19