Random seeds in classic BD games

YouTube · Post by **Arno** » Mon Jun 29, 2020 8:17 pm

When I played BD1 as a child, I noticed that in caves C and L (on level 1), the diamonds/boulders were lying in a similar "random" pattern on the map.

Later on, I discovered more such similarities. For example all caves A in Don Pedro's games show a pattern like cave A of BD1. Same for the C-caves in Don Pedro's games and cave C of BD1.

Nowadays, it is well known that these classic caves use a random generator for random filling of the map, and when 2 caves use the same random seed this results in a similar pattern.
Of course, whether those 2 caves indeed look similar for the player also depends on serveral other factors, like the densities of the filling objects and the presence of other (non-randomly) placed objects.

I've decided to create the following overview table, showing the random seeds of all caves from the classic BD series BD1-11. Here, BD4 is Dr. Watson's game and BD5-11 are from Don Pedro. Note that for BD1 and BD2, the table shows the random seeds for all 5 levels, while for all other games it shows only level 1. A bar (-) indicates that the corresponding cave does not use random filling.

Perhaps this table uncovers some similar patterns that we didn't realize before.

Code: Select all

Cave BD1                 BD2                 BD3 BD4 BD5 BD6 BD7 BD8 BD9 BD10 BD11
A:    10  11  12  13  14  11  12  13  14  15  10   3  10  10  10  10  10    -   10
B:     3   0   1  87  88 100 137 140 251  51   7   3   -   -   -   -   3    3    -
C:     0  50  54  52  55  24  45  52  30  40   1  54   0   0   0   0   0    0    0
D:     0 110 112 115 119   -   -   -   -   - 160   0   -   0   0   0   -    0    -
1:     -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -    -    -
E:     -   -   -   -   -  30  31  32  33  34  17   -   -   -   -   -   -    -    -
F:     0  20  21  22  23  10  11  12  13  14  18   0   -   -   -   -   -    -    -
G:     2   7   8  10   9  10  11  15  13  14  10   2   2   2   -   -   2    2    -
H:     1   3   4   5   6   -   -   -   -   - 170   1   1   1   1   -   -    -    -
2:     -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -    -    -
I:   100 137 140 251  51   -   -   -   -   -  49 100 100 100 100   - 100    -  100
J:     -   -   -   -   -   1   2   3   4   5   -   -   -   0   0 100   -    -    -
K:     0   4 102 151 100  10  11  12  13  15 152   -   0   -   -   -   -    -    -
L:     0  60   2  59 102  12   8   7   9  11  86   0   0   0   0   0   -    -    -
3:     -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   10    -
M:     0   1   2   3   4 137 140 100 251  51 150   -   -   0   0   -   -    0    -
N:     -   -   -   -   -  15  16  17  18  19 170   0   0   0   -   -   -    -    -
O:     1  29  30  31  32   -   -   -   -   - 170   -   1   -   -   -   1    1    1
P:     1 120 129 126 123  10  11  12  13  14  68   1   -   1   1   -   -    1    -
4:     -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -   -    -    -

Dustin · Post by **Dustin** » Wed Jul 01, 2020 9:41 am

Interesting thread!

I played around a lot with random seeds in GDash - which uses the same random generator as the original engines - and one of the first things I did was to check out the BD1 and 2 random seeds and trying to find out why he used these seeds in some caves:

BD1-A: 10 11 12 13 14
Just five consecutive seeds from 10 to 14, indicating that the random seed does not make a big difference in this cave.

BD1-B: 3 0 1 87 88
This looks way more "worked out" than A! Indeed, the random seed does make a big difference here, as on L1, there's only one not-too-dangerous firefly, while on L5 they just fly around everywhere!

BD1-C: 0 50 54 52 55
This is one of the caves that makes me think that PL might first have intended to make a 1L-game and got the idea for the higher levels later on. That's because of the hugh "gap" between the L1 seed and the higher level seeds. Such a thing can also be seen in caves D, F, L, O and P! If so, than it was probably a clever idea to make the game 5 times as big without needing a lot more bytes and bits!
Also I checked and found out why the seeds 51 and 53 were left out - these seeds would simply block off the exit and thereby make the cave unsolvable!

BD1-G: 2 7 8 10 9
BD1-H: 1 3 4 5 6
I find the combination of these two caves interesting. It's striking that the random seeds are completely different, using 1-10 but not 0. I think that the reasons are as follows:
- Caves G and H have few regular objects and almost the same random densities, so using the same seed twice would have led to very similar-looking caves.
- 0 was probably not used because it has already been used quite often (B/2, C/1, D/1, F/1).

BD1-I: 100 137 140 251 51
Completely new random seeds! Thses seem to be PL's favourite seeds for a random boulder-diamond-filling - at least he used the exact same seeds also in BD2-B and M! (In BD2-B, we technically have a boulder-amoeba-random filling, but the amoeba should convert into diamonds anyway, so it's very close to a boulder-diamond-randomization!

)
A striking detail is that I/4 is clearly harder than I/5 - Arno, you even demoed I/4 but not I/5 on this page! So obviously, PL underestimated the difference that the random seeds can make in this cave.

BD1-K: 0 4 102 151 100
Another cave where the difficulty highly depends on the random seed, so it makes perfect sense that the seeds were chosen carefully again

BD1-L: 0 60 2 59 102
Also here, the seeds look carefully chosen. The main reason here might be that many seeds lead to a very easy cave where no diamonds are hidden behind walls and therefore no explosions are necessary! This would of course destroy the whole cave concept, so PL had to test quite a bit to find five well-working seeds. Also, here the similarity between C/1 and L/1 that Arno already mentioned can be seen - both caves use the same seed 0 and also the exact same random fill elements (diamonds, boulder, space) with the same densities!

BD1-M: 0 1 2 3 4
Similar to A - the random boulder filling almost makes no difference, so no reason to waste a lot of time for testing... though as a child, I was quite a bit annoyed by the fact that on L3 and only there, it was not possible to move from the south-west to the south-east corner because of blocking boulders...

BD2-A: 11 12 13 14 15
Comparable to 1A, but why didn't he use 10 here? Well, there's indeed a clear reason: this seed would make the first firefly pre-explode!
Here there's another striking similarity to me - both BD1-a/2 and BD2-A/1 use the seed 11, and both have a huge boulder stack in the north-west corner! However, these boulders made a nice career - in BD1 they just blocked Rockford's way, while here they convert into shiny diamonds!

BD2-C: 24 45 52 30 40
Looks like this was carefully chosen again! And indeed, with such a narrow space the placement of every firefly can make a big difference in difficulty. I actually tested all 256 random seeds of this for "BD2- the expert levels", and I noted that almost every random seed includes at least one stationary firefly which has to be snapped free. However, no snapping is required in PL's five levels, so I wonder if he intentionally avoided this! If so, than the chosen random seeds are almost the only ones from 0-100 where no snapping is strictly required!

BD2-E: 30 31 32 33 34
I'm under the impression that PL underestimated the random seeds in this cave - he just chose five consecutive seeds as in A, but it makes quite a difference where the diamonds fall and the fact that on levels 2 and 5, a boulder falls onto the inbox before Rockford comes out makes those levels a lot safer than the others. For this reason, I find E/5 a lot easier than E/4, similar to BD1-I.

BD2-G: 10 11 15 13 14
Why not 12? Well, I think the reason is that this seed has only six diamonds, which is quite few compared with the other seeds! And then, why not 10 11 13 14 15? Probably because the random seeds 13 and 14 are clearly harder than 15, so PL wanted to keep those seeds for levels 4 and 5.

BD2-K: 10 11 12 13 15
Strikingly, 14 is missing - why? Well, there would be an ugly piece of magic wall below the exit, while otherwise the walls are only below diamonds!

BD2-L: 12 8 7 9 11
10 is somehow missing here, and it's clear why - it's unsolvable! Rockford would be blocked by boulders at the start. IMO, when PL ordered the random seeds, he clearly overlooked the fact that level 3 with seed 7 is way harder than any other level, so I think it should have been level 5.

BD2-N: 15 16 17 18 19
Probably PL wanted some alternation from the seeds 0-14, which he extensively used before! Also here, five consecutive seeds make a lot of sense, because the random fill doesn't really affect the difficulty.

BD2-P: 10 11 12 13 14
This one quite surprised me when I saw it first - I would have thought that the random placement of the diamonds would make a clear difference in difficulty, but PL just chose five consecutive seeds again. But I also think that the five levels aren't worked out here as much as in other caves - for example, I find P/2 a lot easier than P/1. On the other hand, P/5 was indeed the by far biggest challenge to me!

Arno, sorry I didn't fully match your original intention to discover similarities - but as I played around with the BD1 and 2 seeds so often and intensively, I just wanted to share my results!

YouTube · Post by **Arno** » Wed Jul 01, 2020 2:28 pm

Very nice information Dustin! Actually I think it fits very well in this thread!

Next, I'd like to show some examples of cavemaps which show a similar pattern of random filling.

In these examples, not only the random seed is the same, also the densities of the objects are similar enough, and the amount of non-random objects is limited, such that the similarity in random filling is clearly visible.

Seed 10

BD1 Cave A:

BD8 Cave A, same densities:

BD9 Cave A, idem:

And BD2 Cave G, maybe this one is less clear, but at least I remember I've spotted this similarity long before I knew about random seeds and the implementation in BD!

By the way, this similarity exists on all 5 levels, although screenshot shows only level1:

YouTube · Post by **Arno** » Wed Jul 01, 2020 3:24 pm

Seed 0

BD1 Cave C:

BD5 Cave C: walls are just replaced by boulders:

BD9 Cave C: walls just replaced by T-walls:

BD10 Cave C: replacement walls->boulders, boulders->diamonds, diamonds->T-walls:

BD11 Cave C: different densities, but at least the diamonds are lying on the same places:

BD1 Cave L: same densities for boulders and diamonds:

BD5 Cave L: small differences in densities:

BD4 Cave F: fireflies at the location where we used to have diamonds:

BD4 Cave L: idem:

YouTube · Post by **Arno** » Fri Jul 03, 2020 8:56 pm

Seed 1

BD1 Cave H:

BD1 Cave P: I always recognize the upper-left corner with the 2-boulder-stack and the group of 4 boulders next to it:

BD1 Cave M, level 2: similar boulder pattern with the same easily recognizable upper-left corner:

BD4 Cave P: idem:

BD6 Cave P: idem:

BD9 Cave O: idem:

YouTube · Post by **Arno** » Fri Jul 03, 2020 9:08 pm

Seed 3

BD1 Cave B:

BD1 Cave H, level 2: in particular the bottom-right corner is easily recoginzable in this boulder/space pattern:

BD4 Cave A: The attentive player could notice that the first two caves of Dr Watson's BD4 have a similar pattern of boulders:

BD4 Cave B: Same densities of boulders and space as in cave A (but no diamonds):

YouTube · Post by **Arno** » Sat Jul 04, 2020 12:48 pm

Seed 11

This one gives a funny similarity mentioned by Dustin in his post.

BD1 Cave A, level 2: most striking here is the stack of boulders blocking Rockford's way in the top-left corner:

BD2 Cave A, level 1: similar stack above the magic wall, just one boulder less because of the overruling line of dirt above the magic wall:

YouTube · Post by **Arno** » Sat Jul 04, 2020 12:56 pm

Seed 54

BD4 (Dr. Watson) Cave C:

BD1 Cave C, level 3: same map, but with normal walls instead of T-walls:

YouTube · Post by **Arno** » Sat Jul 04, 2020 1:09 pm

I spotted another similarity, yet one of a different kind.

Compare the following two maps:

BD1 Cave C, level 1 (Seed = 0):

BD1 Cave C, level 3 (Seed = 54):

Look at, for example, the pattern at the bottom-right corner of the level 1 map, with the two pairs of diamonds. The same pattern is also visible at the top-left corner of the level 3 map! Apparently, there is some shift in the random pattern when two specific seeds are used!

I'm wondering if this phenomenon could be explained by the working of the C64 random generator...!

By the way, these are all the similarities that I would like to show. If you know some others which I have missed, please chime in!

Dustin · Post by **Dustin** » Sun Jul 05, 2020 12:58 am

One can actually find a lot more of such "seed shifts"! For example, look at the upper right corner of BD1-C/3 (the last map you posted) - can you spot Rockford's "parents" there, the boulders between which he was born in cave A/1?

You can find the same boulder pattern once more in the same map, and also twice in the C/1 map!

In general, there are a lot of regular patterns with the C64 random generator. For the trained eye, it should be easy to spot within seconds whether a given cave map was created with the C64 RNG or not!

Also, there are random seeds which produce very similar cave maps, up to >90% identity! Patterns that I know by heart after years of C64-RNG-usage are:
1. The random seeds 5 and 9 are almost identic, except that they're shifted by one row.
2. The seeds 0 and 19 are very similar. 19 is actually used for BD2-N/5, so it should be possible to compare this random filling with several seed-0-caves!
3. Also 10 and 16 are somewhat similar. 16 is used in BD2-N/2, so perhaps this similarity can be spotted in classic caves as well.
4. As for higher numbers (from about 80 onwards), it happens very often that two consecutive random numbers produce similar or even almost identic maps. That's such a striking effect that I also wondered many times how exactly the C64 generator works! The mathematician in me is curious...

YouTube · Post by **Arno** » Sun Jul 05, 2020 7:31 pm

Dustin wrote:The mathematician in me is curious...

Mine too!

Although it is not a small task to make sense of this series of binary operations...

What we do see quickly is that the algorithm constantly works with 2 numbers between 0 and 255. Using both numbers as input, it draws another pair of such numbers, which in turn are the input for the next draw. After each draw, the first of the 2 resulting numbers is the random number used for the cave filling. For the starting draw, the first number is always zero, while the second number is the random seed as specified for the cave/level.

This could explain the repeating patters, since every time two sequences of random numbers give the same pair at different points (for example, suppose that the pair 139,224 occurs after 286 draws with seed 0 and after 379 draws with seed 52), then from these points onward the continuing sequences of random numbers will be the same.

Other than that, I'm still wondering if this algorithm could explain the typical C64-ish patterns. For example, why do large vertical stacks of boulders occur more often than large horizontal lines of bouders? (Apparently, when a low number is drawn, then 40 draws later (which is the length of a standard cave) it is more probable that another low number is drawn...?)

Dustin · Post by **Dustin** » Wed Jul 08, 2020 7:21 pm

It starts to get really interesting now!

I think the algorithm might be programmed in a way that the values strongly tend to "get mixed" in a way that it's likely that if the first value is very high, it's likely that the next draw gives a lower first number, and vice versa. This would basically mean that large horizontal stacks are unlikely to happen because for this, the first random number would have to be low enough for many draws in a row.
On the other hand, after 40 draws, "everything can happen", which means that vertical stacks aren't that unlikely to happen.

Also the fact that some specific random seeds lead to almost the same cave maps can be explained now. For example, seeds 5 and 9 give almost the same cave but shifted by one row. This would be logical if the pair (0,5) would lead to (0,9) after 40 draws or vice versa!
Well, this explanation isn't 100% perfect because the one-row shift isn't 100% perfect either, but the perfect explanation should definitely go into that direction ;D
Arno, I'll email you the two cave maps of cave C with random seeds 5 and 9, so you could post them here or host them on your site so that I can post them

YouTube · Post by **Arno** » Thu Jul 09, 2020 4:26 pm

Dustin wrote:I think the algorithm might be programmed in a way that the values strongly tend to "get mixed" in a way that it's likely that if the first value is very high, it's likely that the next draw gives a lower first number, and vice versa. This would basically mean that large horizontal stacks are unlikely to happen because for this, the first random number would have to be low enough for many draws in a row.
On the other hand, after 40 draws, "everything can happen", which means that vertical stacks aren't that unlikely to happen.

Well, as I've found out it's actually a combination of "horizontal lines less likely than normally expected" and "vertical lines more likely than normally expected".

I've experimented a bit in my Excel implementation on an extended cave map (still with 40 columns, but with 100 rows instead of 20).
I tried various random seeds combined with the filling rule of BD1 Cave A, in which a non-dirt item is placed when the random value is <60.

My results:
- Probability of a random number <60 (i.e. non-dirt item): 60/256 ~ 23.4%
- Frequency that a number is <60: around 23-24% (that is, indeed near the theoretical value)
- Frequency that the next number is <60 given that the current number is <60: around 18-19% (that is, lower than the expected 23-24%)
- Frequency that the 40th next number is <60 given that the current number is <60: around 38-40% (that is, way higher than the expected 23-24%)

Combining these observations, you can conclude that there is indeed a tendency for vertical lines of non-dirt items!
I also have an explanation based on the working of the PRNG, but I will write a separate post about that topic later on.

Dustin wrote:Also the fact that some specific random seeds lead to almost the same cave maps can be explained now. For example, seeds 5 and 9 give almost the same cave but shifted by one row. This would be logical if the pair (0,5) would lead to (0,9) after 40 draws or vice versa!
Well, this explanation isn't 100% perfect because the one-row shift isn't 100% perfect either, but the perfect explanation should definitely go into that direction ;D

Indeed. For these two seeds, the sequence starts getting identical after a different number of draws. Below pictures (which you sent me yesterday) show the resulting maps when using the filling rules of BD1 Cave C:

Seed 5:

Seed 9:

The yellow lines (which I added) indicate the dirt-position from which that random numbers start being identical.
- Seed 5: For draw no. 153, the input (Seed1, Seed2) is (124, 121), and the output is (185, 12).
- Seed 9: For draw no. 113, the input (Seed1, Seed2) is (251, 121), and the output is (185, 12).
In this case, the differece between both draw counters is 153-113 = 40, which gives exactly one row shift.

Before that point there are still some similarities, but the numbers are not identical, so the maps show differences at various points.

At Krissz' site, Nesdori has written some extensive analysis about this phenomenon, which I will also share in a separate post.

YouTube · Post by **Arno** » Fri Jul 10, 2020 9:51 am

I hereby share a comment by Nesdori on Krissz' site about the presumed origin of the PRNG (=pseudo-random number generator) that is used in BD to generate random cave maps:

I checked some publicly available PRNG from 70's and 80's and they were more complex and in sense of randomness better quality than the BD RNG. But they were also slower because they usually had a loop where bits were twiddled. If I had to guess, I would say that Liepa wrote the RNG just for Boulder Dash. It had to be fast because cave generation shouldn't take too long and although slime wasn't yet introdused in BD1, maybe Liepa already had the idea of in mind so that the RNG should be fast enough also to be called during the scan multiple times which is even more time critical than cave generation.
if Arno ever does "Peter Liepa interview part 2", there are a lot of technical questions already on the list.

And here's another great analysis by Nesdori about the various pairs of initial seeds which lead to partly identical cave maps:

I checked randomfill with all initial seeds against all other initial seeds to find all colliding pairs of initial seeds so that during 800 randomfill calls the complete seed (combination of seed1 and seed2) is same at some point which of course causes all the rest seeds to be same until randomfill is finished. There are surprisingly many of those seed collisions, for example for initial seed 0, there are 186 other initial seeds that at some point have the same complete seed during 800 calls. And it's the same thing for other seeds. So the initial seeds really are mangled together and it's more probable that two seeds collide during 800 calls that they aren't colliding!

Because there are so many seed collisions the complete list would be very long. So i decided to list top 5 seeds for all seeds which have the biggest number of same complete seeds during randomfill. Here's the first line of the set, the best collision for seed 0, the well-known 0,19 seed pair.

seed 0 offset 1 - seed 19 offset 0, x:-1 y:0 799

Offset means how many times the rng has to be called until the collision is caught [small correction: because the rng is always called once before the value is used the number or calls is actually offset + 1]. So in this case seed 0 has to be called once and seed 19 not at all to get a collision. That's because if the call the rng with seeds 0 0 the result is 0 19. Usually the colliding seed is not any of the initial seeds but the rng has to be called with both initial seeds few times to get a collision. x and y are the location offset for the latter seed and it tells how many y and x steps the other cave layout is off. The last number is the number of same seeds during complete randomfill with 800 calls. it's actually (800 - the bigger of the offsets). This is the value where the top list rating is based. So the longer the shared sequence of seeds is during randomfill, the higher the pair is on the list.

There are some surprising new unknown seed pairs on the top list where the x-offset is quite big so they have been harder to spot than those seed pairs where the cave layout is just of a little. Also some of the known pairs didn't make it to the top list. Dustin mentioned pair 5, 9 but it didn't make it to the top list for seeds 5 or 9. Here's the info line for 5, 9 pair:

seed 5 offset 152 - seed 9 offset 112, x:0 y:-1 648

So initial seed 5 has to be called 152 times and 9 112 times to get a collision. And that's why 112 first values (and so probably objects too) on first lines are different. 648 seeds out of 800 are same and it's quite high ratio but pair 5,9 gets still gets only rank #20. There are 19 initial seeds which share more seeds with initial seed 5 than seed 9! For comparison, here's the top 20 list for seed 5:

seed 5 offset 29 - seed 122 offset 3, x:-26 y:0 771
seed 5 offset 10 - seed 129 offset 30, x:20 y:0 770
seed 5 offset 10 - seed 240 offset 31, x:21 y:0 769
seed 5 offset 32 - seed 238 offset 0, x:-32 y:0 768
seed 5 offset 10 - seed 199 offset 53, x:3 y:1 747
seed 5 offset 10 - seed 172 offset 61, x:11 y:1 739
seed 5 offset 62 - seed 137 offset 2, x:-20 y:-1 738
seed 5 offset 88 - seed 239 offset 16, x:8 y:-2 712
seed 5 offset 10 - seed 209 offset 99, x:9 y:2 701
seed 5 offset 10 - seed 24 offset 102, x:12 y:2 698
seed 5 offset 10 - seed 84 offset 112, x:22 y:2 688
seed 5 offset 10 - seed 153 offset 115, x:25 y:2 685
seed 5 offset 129 - seed 48 offset 14, x:5 y:-3 671
seed 5 offset 10 - seed 212 offset 132, x:2 y:3 668
seed 5 offset 10 - seed 6 offset 136, x:6 y:3 664
seed 5 offset 10 - seed 17 offset 142, x:12 y:3 658
seed 5 offset 10 - seed 254 offset 143, x:13 y:3 657
seed 5 offset 10 - seed 236 offset 144, x:14 y:3 656
seed 5 offset 10 - seed 196 offset 146, x:16 y:3 654
seed 5 offset 152 - seed 9 offset 112, x:0 y:-1 648

and here is the complete top 5 list for all initial seeds (still quite a long list )

seed 0 offset 1 - seed 19 offset 0, x:-1 y:0 799
seed 0 offset 8 - seed 141 offset 14, x:6 y:0 786
seed 0 offset 8 - seed 123 offset 15, x:7 y:0 785
seed 0 offset 27 - seed 93 offset 9, x:-18 y:0 773
seed 0 offset 28 - seed 160 offset 13, x:-15 y:0 772

seed 1 offset 1 - seed 148 offset 0, x:-1 y:0 799
seed 1 offset 10 - seed 157 offset 35, x:25 y:0 765
seed 1 offset 41 - seed 248 offset 15, x:14 y:-1 759
seed 1 offset 10 - seed 18 offset 49, x:-1 y:1 751
seed 1 offset 55 - seed 70 offset 5, x:-10 y:-1 745

seed 2 offset 12 - seed 46 offset 43, x:-9 y:1 757
seed 2 offset 12 - seed 241 offset 46, x:-6 y:1 754
seed 2 offset 47 - seed 249 offset 1, x:-6 y:-1 753
seed 2 offset 54 - seed 65 offset 11, x:-3 y:-1 746
seed 2 offset 12 - seed 28 offset 77, x:25 y:1 723

seed 3 offset 4 - seed 150 offset 3, x:-1 y:0 796
seed 3 offset 13 - seed 126 offset 0, x:-13 y:0 787
seed 3 offset 16 - seed 68 offset 6, x:-10 y:0 784
seed 3 offset 48 - seed 56 offset 12, x:4 y:-1 752
seed 3 offset 72 - seed 41 offset 17, x:-15 y:-1 728

seed 4 offset 8 - seed 234 offset 16, x:8 y:0 784
seed 4 offset 45 - seed 166 offset 10, x:5 y:-1 755
seed 4 offset 8 - seed 57 offset 65, x:17 y:1 735
seed 4 offset 69 - seed 92 offset 18, x:-11 y:-1 731
seed 4 offset 8 - seed 30 offset 73, x:25 y:1 727

seed 5 offset 29 - seed 122 offset 3, x:-26 y:0 771
seed 5 offset 10 - seed 129 offset 30, x:20 y:0 770
seed 5 offset 10 - seed 240 offset 31, x:21 y:0 769
seed 5 offset 32 - seed 238 offset 0, x:-32 y:0 768
seed 5 offset 10 - seed 199 offset 53, x:3 y:1 747

seed 6 offset 0 - seed 254 offset 7, x:7 y:0 793
seed 6 offset 2 - seed 17 offset 8, x:6 y:0 792
seed 6 offset 8 - seed 212 offset 4, x:-4 y:0 792
seed 6 offset 42 - seed 84 offset 18, x:16 y:-1 758
seed 6 offset 42 - seed 153 offset 21, x:19 y:-1 758

seed 7 offset 20 - seed 185 offset 4, x:-16 y:0 780
seed 7 offset 20 - seed 217 offset 9, x:-11 y:0 780
seed 7 offset 21 - seed 224 offset 3, x:-18 y:0 779
seed 7 offset 30 - seed 74 offset 0, x:-30 y:0 770
seed 7 offset 0 - seed 103 offset 48, x:8 y:1 752

seed 8 offset 5 - seed 191 offset 22, x:17 y:0 778
seed 8 offset 5 - seed 78 offset 28, x:23 y:0 772
seed 8 offset 65 - seed 6 offset 12, x:-13 y:-1 735
seed 8 offset 65 - seed 17 offset 18, x:-7 y:-1 735
seed 8 offset 65 - seed 212 offset 8, x:-17 y:-1 735

seed 9 offset 34 - seed 190 offset 18, x:-16 y:0 766
seed 9 offset 9 - seed 88 offset 38, x:29 y:0 762
seed 9 offset 9 - seed 73 offset 52, x:3 y:1 748
seed 9 offset 9 - seed 79 offset 65, x:16 y:1 735
seed 9 offset 73 - seed 32 offset 12, x:-21 y:-1 727

seed 10 offset 0 - seed 250 offset 14, x:14 y:0 786
seed 10 offset 21 - seed 112 offset 9, x:-12 y:0 779
seed 10 offset 21 - seed 163 offset 13, x:-8 y:0 779
seed 10 offset 21 - seed 171 offset 6, x:-15 y:0 779
seed 10 offset 2 - seed 127 offset 69, x:27 y:1 731

seed 11 offset 10 - seed 34 offset 22, x:12 y:0 778
seed 11 offset 28 - seed 131 offset 15, x:-13 y:0 772
seed 11 offset 14 - seed 106 offset 29, x:15 y:0 771
seed 11 offset 30 - seed 205 offset 0, x:-30 y:0 770
seed 11 offset 14 - seed 77 offset 37, x:23 y:0 763

seed 12 offset 1 - seed 94 offset 10, x:9 y:0 790
seed 12 offset 25 - seed 165 offset 17, x:-8 y:0 775
seed 12 offset 0 - seed 92 offset 29, x:29 y:0 771
seed 12 offset 0 - seed 166 offset 45, x:5 y:1 755
seed 12 offset 65 - seed 203 offset 2, x:-23 y:-1 735

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YouTube · Post by **Arno** » Fri Jul 10, 2020 9:54 am

... and the remainder of the list:

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