Patterns in the art of Chess

Nature uses only longest threads to weave her patterns, so that each small piece of her fabric reveals the organisation of the entire tapestry - Richard Feynman

This article springs from the passion exuded by a young kid - Sai Akhil Anand - and his quest for discovering patterns (and express them as wonderful paintings) in almost everything that he sees and comes across even in his tender age! His world revolves around Hemchand sequence (otherwise known as Fibonacci sequence), Sierpenski triangle, Golden ratio, Fractals.... so on and so forth and his canvas encompasses a vast arena ......from the trail of snail on the floor to the trail a rocket leaves on the stratosphere!

Patterns are wonderful and enhances creativity, as long as it is used like we use salt in our food - nothing more nothing less! Patterns act as catalyst in the process of understanding the art and showcasing it by enhancing the creativity of the artist in his or her own unique way! 

"Our humanity rests upon a series of learned behaviours, woven together into patterns that are infinitely fragile and never directly inherited" says Margaret Mead, an anthropologist. Infinitely fragile - because the pattern breaks apart if overused and most importantly if it is not perceived in proper manner.... if its sanctity is spoiled by overexposure. Pattern - is a masculine word.... as it has its root from "paternity" - "patr" in latin means father. 

While explaining the pattern in one of the painting of Akhil, the proud father, legendary Vishy remarked how it obeys the golden ratio and the ever increasing spiral (for eg; the pollen and petal formation in Sun flower) increases the surface area of exposure! 

That ever increasing surface area of the spiral at a macro level, corresponds to Hemchand sequence - the infinite sequence which also corresponds to fractals - that logarithmic spiral - which gets into infinitely smaller scales.

At an infinitely smaller level, the pattern remains unexposed and nature uses that to protect and preserve her greatest secrets.

Well, one prominent pattern which manifests in the art of Chess is Fractals! One is tempted to say that the Hemchand sequence should correspond to chess as the sequence is a product of the preceding two numbers and you may relate it to the move by you and your opponent or vice versa!

But Chess is far more intricate and infinitesimally beautiful to merely fall into the realms of just two previous moves and its arithmetic progression! 

Fractals reveals its beauty as you zoom into it deeper and deeper with its fascinating self perpetuating patterns but that which is not apparent superficially where it appears as irregular structure.  

I give below a TED talk by the mathematician Benoit Mandelbrot whose work lead the world to understand fractals in deeper manner and its application in various fields of research.

A game of chess reveals its beauty as you delve deeper into it with an unconditional eye - a feel for what it reveals or conceals and not to try and force things by effort - calculation! As William Lombardy observed, "calculation is an emergency situation in a game of Chess". 

Pattern in chess is self effacing in nature!

 

The above two positions are separated almost by a century! Can you see the pattern!? Not without reasons the square f7 (and f2) is considered the weakest on the Chessboard!

The first one is Dmitry Andreikin vs Magnus Carlsen played in 2003 and the second one is between Mikhail Chigorin vs Akiba Rubinstein played in 1906!

I purposefully refrained from comparing Chigorin vs Rubinstein with exactly same pattern which happened in Lundin Vs Smyslov, Staunton Memorial, 1946. for the reasons, that, Chess patterns need not have the same pieces, but one needs to feel the pattern in the spirit of the position and not merely its components!

For academic sake, the following is that position where, strangely Smyslov failed to play the move 37.....Rf2 and instead took a draw by repetition 37.....Nf2?

The play by Magnus in his game against Andreikin is exemplary. I am sure I would have dealt with this game in one of my earlier articles as it was a pure work of art by a 13 year old! Even at the cost of repetition I shall reproduce the transition phase.

Andreikin vs Carlsen, WC U-14, 2003

18.....Bh6!

An obvious move which holds an eye on f4, pins the pawn and.....

19.Ne3 Qb6; 20.Kh1 Qc5!!

A manoeuvre which is very reminiscent of Janowsky vs Rubinstein - not the move per say, but the idea of provoking weakness and attacking the weakness - another pattern!

21.b4

Black was intending to push b4 and then allow the Rook to enter the seventh rank, probably after a preliminary .....Rfc8, adding pressure on c3 square and make Rooks invasion more effective!

21......Qc7!?

The move Qc5's purpose is over! Not 21.....ab4? 22.cb4 Qb6 23.Rac1=

22.Rad1 Rbc8! 23.ba5

23.Qd6 Qc3 24.Rd3 Qb4 25.Qb4 ab4 and White has too many weakness and Black's Bishops and Rook are very actively attacking them!

23.....Qa5 24.Qd6 ef4 25.gf4 Qa2 26.Qe5 g6!

.....and the Bishop enters the game through different route!

27.Qb5?! Rc3 28.Nd5 28....Bh3!! 

.....and we will reach the position that is given in the beginning in a couple of moves!

Perhaps a reverse move order.... 27.Nd5 Bd5 28.ed5 Bg7 was a better option..... perhaps!

Fractals in nature is about zooming down further and further into the irregular shapes which are prevalent in nature and one observes that the patterns repeats beautifully. In chess it is more like a combo of Rorschach inkblots and fractals - each and every move a side plays is like spilling an ink drop which creates a vivid pattern when it is folded and unfolded. A chess position reveals various patterns which perhaps would resemble something from the past, known...unknown.... in a subtle manner, as one probes deeper and deeper. 

Even within a game, patterns may keep repeating with slight differences at various stages, where, an addition or omission would create a distinctly different flavour in the pattern that is repeated!

For eg, I shall give a few positions below:

First set of positions:

Mortensen vs Karlsson, Esbjerg, 1988

Black is suffering badly! 

But the art of Chess or for that matter any art, rests in not rushing but waiting! For a Cricket analogy, the Batsman has to wait to allow the ball to do everything and then meet it at the last possible moment - which is only 1/4 of a second perhaps! 

White assumed that his King is absolutely safe, tucked in that side where no activity is 'possible' immediately and therefore rushed to play 20.Rh3??

I leave it to the reader to discover why this almost an obvious move - a blunder! This move should be preceded by a move which defends the fortress.

..... and how that pattern is represented in the following position...!  

Pervakov

White to play

In the above study by Pervakov, the solution runs to 14 moves, but the moves are self evident as they are forced and you can see repeating patterns within as you solve. But, the significant difference between a win or loss for White happens on the first move! Every other move thereof is the same!

In both the above position, the first move is significant which determines a loss or win and the attack happens on that same square!

Second set of positions:

A similar pattern is involved in the following studies created by Elkies! and by Chicco. In both the following positions, the first move determines whether White wins or Black manages a draw.

Elkies

White to play

And observe for yourself how the pattern from Elkies manifests in the following study by Chicco!

Chicco

White to play

Third set of positions:

The pattern in the following two positions is very obvious as the nature of position is also strikingly similar.

Winants vs Guris, Belgium, 1992

White to play

Riga vs Oryol, Olginka, 1986

White to play

Fourth set of positions:

Belsitzman vs Rubinstein, Warsaw, 1914

Black to play

The first move in the above position is the last move in the next position - a patter of its kind with a similar finish!

Maister vs Grozdov, Corres, 1954

Black to play

I am not giving the solutions and sure the reader would solve them and derive joy! I can keep going on and on with various examples! But somewhere I have to conclude and let me conclude with an interesting story which happened in 1991.

During Iraq war in 1991, one fine morning on 24th February, Michael Riley, Lieutenant Commander onboard the HMS Gloucester - a British destroyer stationed about 15 miles from the port to protect the Allied fleet by monitoring the airspace surrounding that area, had an important decision to make, which had huge consequence!

Riley had been on duty since midnight and at 5:01 in the morning, just as the Allied ships began shelling Ash Shuaybah, he noticed a radar blip off the Kuwaiti coast. A quick calculation of its trajectory had it heading straight for the convoy. Although Riley had been staring at similar looking blips all night along, there was something about this Radar trace that immediately made him suspicious. He couldn't explain why, but the blinking green dot on the screen filled him with fear!

He continued to observe the incoming blip for another 40 seconds as it slowly honed in on the USS Missouri, an American battleship. With each sweep of the radar, the blip grew closer. It was approaching the American ship at more than 550 miles per hour.

If Riley was going to shoot down the target - as he suspected - then he needed to respond right away. If that blip was a missile from enemy and Riley did not act immediately, it would be too late; hundreds of sailers would die, the USS Missouri would be sunk and Riley would have stood by and watched it happen.

But Riley had a problem as the same airspace was frequented by American A-6 fighter jets and the laser guided antimissile could as well be shooting down an A-6 and with it two innocent pilots of allied force!

The target was moving fast. The time for deliberation was over. Riley issued the order to fire two Sea Dart surface to air missiles to confront the approaching blip! The blinking green blips appeared to be drawn to the target, like iron filings to a magnet. Riley waited for the interception. 

The explosion echoed over the ocean and all the blips immediately disappeared from the radar screen. Whatever had been flying towards the USS Missouri helplessly fell into the sea, just 700 yards in front of the American Battleship. 

A few moments later, the captain of the HMS Gloucester entered the radar room and asked Riley, "Whose Bird is it?" Riley responded, "It was ours Sir". The captain asked how he can be so sure. Rile said that he just knew!

The next 4 hours were the longest ones of Riley's life. If he had shot down an A-6, then he would have killed two innocent pilots along with destroying the fighter craft. His career would have abruptly ended and he may even be court-martialed. 

Few hours later, the captain came with the news, the radar blip was in fact a silkworm missile and not an American fighter jet and that Riley had single handedly saved a battleship and hundreds of sailers!!

For years, this case was studied to find out how Riley was able to come at that decision with such an insufficient data....merely on the hunch which reflected upon a certain pattern that he merely felt but that which he could not articulate enough on "why"?!

A chess game is a dual between two minds! How well and sharply one observes such blips and its nature, and either allow or counterattack targets....etc, determine the subsequent play..... and perhaps the outcome at large!

The connect to this article on chess patterns with Chess as an art and the patterns that Akhil discovers when he sees or observes anything that he comes across is that, patterns are repetitive but with differences and it is that difference which drives Akhil to see more patterns and gives rise to his new and varied artistic creations perpetually! Repetition and Difference is integral to mastering any art! 

Every well played game is interwoven with so many fine patterns that reveals the beauty inherent in Chess in myriad ways!

I remain!