In 1986 we wrote a parallel Mandelbrot program in assembly instructions in the 2K or 4K on-chip SRAM of 17 x T414 Transputer chips linked together with 4 x 10 Mbps links each into a cheap supercomputer [1]. It drew the 512 x 342 pictures on a Mac 128K as terminal at around 10 seconds per picture.

I later wrote the quadruple-precision floating-point calculations in microcode [2] to speed it up by a factor of 10 and combined 52 x T414 with 20 x T800 Transputers with floating point hardware into a larger supercomputer costing around $50K.

With this cheap 72 core supercomputer it still would have taken years to produce the deep zoom of the Mandelbrot set [4] that took them 6 months with 12 CPU cores running 24/7 in 2010 [3]. In 2024 we can buy a $499 M4 Mac mini (20-36 'cores') and calculate it a a few days. If I link a few M4s together with 3x32 Gbps Thunderbolt links into a cheap supercomputer and write the assembly code for all the 36 cores (CPU+GPU+Neural Engine) I can render the deep zoom Mandelbrot almost in realtime (30 frames per second).

That is Moore's law in practice. The T414 had 900,000 transistors, the M4 has 28 billion transistors at 3nm (31.111 times larger at 50% of the price).

The M2 Ultra with 134 billion transistors and M4 Max (estimate 100 billion transistors) are larger chips than a M4 but they are relatively more expensive then the M4 so it is cheaper and faster to link together 13 x M4 than buy 1 x M2 Ultra or 6 x M4 instead of 1 x M4 Max.
Cerebras or NVidia also make larger chips, but again, not as cheap and fast as the M4. Price/performance/Watt/dollar is what matters, you want the lowest energy (OPEX) to calculate as many floating point numbers as possible at the lowest purchase cost (CAPEX), you do not want the fastest chips.

You will want to rewrite your software to optimize for the hardware. Even better would be to write the optimum software (for example in variable precision floating point and large integers in Squeak Smalltalk) and then design the hardware to execute that program with the lowest cost. To do that I designed my own runtime reconfigurable chips with reconfigurable core and floating point hardware precision.

I designed a 48 trillion transistor Wafer Scale Integration (WSI) at 3nm with almost a million cores and a few hundred gigabyte SRAM on the wafer [5][6]. This unchipped wafer would cost around $30K. It would cost over $130 million to manufacture it at TSMC. This WSI would have 1714 times more transistors but cost only 60 times at much, a 28 times improvement, but it is an Apples and oranges comparison. It would be more like a 100 times improvement because of the larger SRAM, faster on-chip links and lower energy cost of the WSI over the M4.

The largest fastest supercomputers [7] cost $600 million. To match that with a cluster of M4 would cost around $300 million. To match it with my WSI design would cost $140 million total. For $230 million you get a cheap 3000 x WSI = 144 quadrillion transistor supercomputer immersed in a 10mx10mx10m swimming pool that is orders of magnitude faster then the largest fastest supercomputer and it would be at orders of magnitude lower cost, especially if you would run it on solar energy only [8], even if you would buy three 3000 wafer scale integration supercomputers ($410 million) and only run it during daylight hours and space it evenly around the equator in cloudless deserts. Energy cost dominates hardware costs over the lifetime of a supercomputer.

All the numbers I mentioned are rounded off or estimates, to be accurate requires me to first define every part of the floating point math, describe the software calculations exactly, make accurate hardware definitions and would take me several scientific papers and several weeks to write.

[1] https://www.bighole.nl//pub/mirror/homepage.ntlworld.com/kry...

[2] https://sites.google.com/site/transputeremulator/Home/inmos-...

[3] http://fractaljourney.blogspot.com

[4] https://www.youtube.com/watch?v=0jGaio87u3A

Maybe https://www.youtube.com/watch?v=zXTpASSd9xE took more calculations, it is unclear.

[5] Smalltalk and Self Hardware https://www.youtube.com/watch?v=vbqKClBwFwI

[6] Smalltalk and Self Hardwarehttps://www.youtube.com/watch?v=wDhnjEQyuDk

[7] https://en.wikipedia.org/wiki/El_Capitan_(supercomputer)

[8] https://www.researchgate.net/profile/Merik-Voswinkel/publica...