This is the fifth post in the series, describing new lands in versions 9.x. We will start with the three lands added in 9.0, all of which have a significant Norse theme.
If you are learning about hyperbolic geometry from popular mathematical sources,
one of the first things you learn is how the sum of the angles of the triangle is
less than 180 degrees. This affects the gameplay -- in fact, this is the reason
why the world is often rotated differently when you return to the same location --
but for a long time I wanted to create a land which requires a bit more understanding of this phenomenon,
where the player has to learn how to calculate the defect quickly.
Burial Grounds is such a land. The original inspiration for the theme was
the Barrows from Lord of the Rings; however, we have read that the Barrow Wights here
were inspired by Draugar from the Norse mythology, and we have decided to use Draugar
directly. Draugar were also one of the interesting monsters in Ragnarok/Valhalla.
One more ingredient is missing here -- since the land requires Orb of the Sword,
how does one obtain it in the first place? This is solved by another land, the
Kraken Depths. The idea of an underwater land where Orb of the Fish is
necessary to do anything comes from the ideas thread
(Fulgur14's post, I think there were also similar ideas by other people). The Kraken appears to be
the widest creature that can move in the hyperbolic plane in a reasonable way,
and its movement foreshadows the Orb of the Sword. Krakens come from the Norse legends,
thus making the Living Fjord, Kraken Depths, and Burial Grounds a sequence
of lands which are different, but yet thematically and mechanically related.
It was previously said how the Elemental Planes were designed because there were already
several Elementals of various kinds. Trollheim is the same, but for Trolls.
Some time in the future we might see a land of birds, a land of canines, or a land
of sharks. :) In many lands, the Trolls are monsters which aim to hurt the player,
but they usually end up actually helping them; again in Trollheim,
you have to use the Trolls' special wall-creation property to your favor.
The name Trollheim is made to sound typical to Norse mythology (like Jotunheim,
the land of giants). We have been searching for an appropriate
"troll treasure" but we could not find anything too exciting -- one weird idea
was to have "golden crowns", inspired by a popular Polish song which says "twelve heavy crowns of pure gold
adorn my head" -- ultimately we have chosen the "golden eggs", referring to the first troll treasure you find (Gold);
people who have played Colossal Cave Adventure should also notice and understand another reference.
Some time after version 9.0 has released, I have received an information from Steam
about the Halloween sale event, aimed at the games with Halloween-like themes.
At first, I did not want to participate in this -- HyperRogue had some monsters which
fit the theme,
but this was not the general theme of the game; adding a Halloween land would be redundant
and probably not that exciting from the event's point of view.
However, I was working on the spherical geometry mode
at the time. Spherical geometry is very different from hyperbolic -- it is bounded,
which allows interesting resource management -- and I thought that a new land specific
for this geometry would be great; and Halloween fit perfectly, with the natural
motivation for being played on a sphere (surface of a jack'o'lantern).
The Dungeon is based on
a post of wonderfullizardofoz, to get more mileage of the new 3D perspective in
the gravity lands. It takes the general idea
of a gravity trap land, skeletons, and ghosts; also Slime Molds as a treasure (a reference
to a food item in Rogue -- I had no other ideas for treasure anyway).
Banshees were replaced by my own idea
(bats, which I have invented some time earlier as a weaker version of Eagles, but I had
no good idea where to put them). Since Skeletons were there, this made sense as an
extension of the Palace (with some influence from
an earlier idea of Fulgur14) -- especially that the mechanics of pressure plates
from the Palace could make an interesting return in a gravity land. The Orb of Recall
comes from the first post in the Orb idea thread,
by wonderfullizardofoz and Fulgur14. (Ideas for new orbs and enemies are welcome, not only for lands!) As a fan of Steven Universe, Fulgur14 expected Amethysts in HyperRogue since Pearls and Garnets were there -- but gem names are just gem names, mostly.
The general idea for the Mountain comes from the same post of wonderfullizardofoz.
Before implementing these two lands, I have already implemented the Orb of Nature,
and I wanted to put it in some land. Since wonderfullizardofoz's idea already included
the Eagles, I have decided to include Ivy too (and make it possible to use the dormant
Ivies to climb the mountain), and make it a subzone of the Jungle.
Long time ago, tricosahedron posted his idea
of a land inspired by Reptiles by M.C. Escher.
The idea was very interesting, but I did not believe that Escher's pattern could be
adapted to hyperbolic geometry -- it seemed that something had to have a threefold or
sevenfold symmetry, and thus look nothing like a reptile. Some time later, tehora said
she wants a land where reptiles rise from the floor as in Escher's work, and I have decided to try harder -- and obtained quite
a nice reptile tesselation -- with some gaps with threefold symmetry as expected, but still, they
did not make the tesselation bad. To the surprise of tehora, the release post listed
this as based on an idea of tricosahedron (I thought she was referring to
tricosahedron's idea, but apparently she had the same idea independently).
Reptiles by M.C.Escher depicts not only the Reptiles themselves, but also
many other interesting things; probably the most interesting one is a dodecahedron,
so it has been chosen as the treasure of this land. (We also collect dice -- from the standard ones based on Platonic solids, to more exotic ones -- so collecting dodecahedra feels very nice to us.)
Contrary to HyperRogue, David Madore's hyperbolic maze
does not take place in the full infinite hyperbolic plane, but rather a finite
part of it (of size of 88110 tiles) whose edges has been stitched together, to make
a space without boundaries; stitching is done in a very regular way, based on matrices
over a finite field. For 9.4 I have decided to implement something similar to Madore's
method -- even though the most unique things about HyperRogue is its infinite and
exponentially expanding world, a special geometry where the world is actually finite
could make for an interesting educational feature, and it could be also used as a
pattern -- similar to the existing Vineyard, Zebra and Palace patterns, but very huge
compared to them (huge, yet highly regular, though in a rather incomprehensible way).
The pattern of 5676 heptagons (18920 cells in total) was big enough to fit large
circles and multiple non-crossing straight lines -- so for the first land based on
this pattern I have decided to use
wonderfullizardofoz's idea of Amazon River, where you have to cross a river without touching the
crocodiles in it, who just go with the current without pursuing you, unless you are
on adjacent cell; however, I have decided that a river land with objects moving with
the current felt too similar to the Whirlpool, so I have rethemed it as the Prairie,
where you have to get on the other side of a herd of charging beasts. Of course, both ideas
-- crossing a road filled with cars, and a river filled with crocodiles -- have been used
classic game Frogger (hotdogPi
also had a similar idea, but when Prairie was already there.) Previously I was thinking
to do this not on a bundle of straight lines/equidistants, but on a bundle of
randomly generated adjacent curves -- maybe such a land will be added in the future.
The regular pattern turned out to have one more interesting property: after placing the
charging paths and the Great Walls (also incorporated in the pattern), it allowed yet
another straight line, which was far away from both the charging paths and the Great
Walls. I have tried to put another charging path there at
first, but this did not work well because of a different structure of the central
straight line; thus, since this line was separate from everything, I have decided to
make it a "safe spot", with no monsters appearing, an alternate source of Orbs of
Safety, and an interesting property that these Orbs of Safety throw you into a location
which looks exactly the same. And what kind of treasure could one find in the prairie,
on the other side (of the herd of bulls)? Of course, the grass is always greener on the other side.
Yet another idea that many different people came up with independently was a land
based on the Boulder Dash
game from 1984 (some readers might know newer games heavily inspired by Boulder Dash,
such as Emerald Mine or Supaplex, or their open source combination, Rocks'n'Diamonds). Like roguelikes, Boulder Dash is grid based
and turn based -- however, turns happened automatically and very quickly, making it
more about timing the keypresses precisely (like a very fast version of Crypt
of the NecroDancer...). One of the iconic features of Boulder Dash were Butterflies,
who did not pursue the player -- they simply moved along the walls -- and
turned into a 3x3 square of Diamonds when killed by a falling boulder;
I thought that an interesting HyperRogue land could be based on this, and so thought
Simon Clarkstone. However, it was not clear how should the gravity be implemented
(like in Ivory Tower or like in Dungeon? where should the boulders fall if there are
multiple choices? how should this work in the HyperRogue grid in general?), so I
have decided to replace gravity with charging bulls -- together with the Prairie,
the 9.4 update was all about Bulls. A later update added a special tiling,
heavily inspired by
(No. 70) by M. C. Escher, and its
hyperbolic version by Doug Dunham -- however, the butterflies had to be "broken"
a bit to make the lines separating tiles clear. Since "diamonds" were already taken,
another gem name had to be chosen -- the name spinel comes from the Latin spina
(arrow), but sounds a bit like the English word spin too, so spinels are appropriate
for gems obtained by shooting bulls at the spinning butterflies.
The Crossroads V are also based on an old idea -- this time
an idea of Fulgur14,
so old that it was called Crossroads III at the time. :) Not sure why this was not
Some people consider HyperRogue to be a hard game. I think that HyperRogue is as hard
as it needs to be -- if it
was easier, it would not force the player to learn. When Ptolemy I asked Euclid
if there was a shorter road to learning geometry than reading Euclid's Elements,
he replied that There is no royal road in geometry; I believe the same is
true not only with mathematics, but also with games such as Chess, Go, or HyperRogue.
Furthermore, just as most players of Chess or Go player do not have hope to every
beat the grand master, many people play difficult roguelikes without caring
about whether they will ever win -- this is because the point of roguelikes is not
necessarily to win, but to have fun while playing a complex game, and getting
better and better in it. This is similar to what Carl Friedrich Gauss
said in a letter to Farkas Bolyai:
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
Gauss and Bolyai have been discussing the nature of parallellness,
and whether it is possible ot prove Euclid's fifth axiom from the other ones, for
a long time without success; many years later, Bolyai's son, János, has discovered the hyperbolic geometry,
and then they learned that Gauss has discovered the same things on its own, but he did not publish the results.
Hyperbolic geometry was also independently discovered by Nikolai Lobachevsky,
who is quoted
to write There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world
-- and indeed, non-euclidean geometry has found many applications, for example in physics, and more recently in art
(M.C. Escher), game design, data visualization and social network analysis; and even HyperRogue itself can be applied as a powerful engine
to work with applied hyperbolic geometry (see RogueViz).
Speaking of M.C. Escher, here is a quote of him: We live in a beautiful and orderly world, not in a chaos without norms, as
we sometimes seem to, which is also relevant to HyperRogue -- as an important thing that sets it apart from other geometrically
weird games, such as Antichamber or Monument Valley,
is that HyperRogue's geometry, although weird, is completely logical, and can be reasoned about; and gaining a deep understanding
of this geometry is important for the game, and why it needs to be hard.
In our opinion, Monument Valley is very easy compared to HyperRogue, but also it is more shallow mathematically, which does not prevent
Monument Valley and Escher's works it is based on to be great works of art.
Which brings us back to the start of this long paragraph.
Since all these classic quotes not only come from people whose work was very important for the development of HyperRogue, but are also
very relevant to the game itself, they have been added as the Knights of Camelot's lines in HyperRogue 9.1.
(Interestingly, if you want to get from A to B in the world of HyperRogue, there is a "royal road",
one such that every other path is significantly longer than it...)
It was not mentioned
in the last part, but since 8.3, the
Knights end their speech in the way similar to
one used by Sprite Guard in his YouTube channel.
It is not known what new features will be added in versions 10.x and described in the next post in this series. So, until then,
thank you very much for reading, and have a great rest of your day!