If you wanted to make a secure password the best way is to use a phrase you made up no one knows. This means you will be able to remember it, it is highly secure, and very difficult for someone to duplicate.
"The red fish went to the store and got me an apple no a pear"
The entropy on that sentence is very high despite many of the letters being the same. If passwords in the future allowed you to use pictures or combinations of words/phrases, entropy increases INSANELY:
For example:
I am five feet
OR
iaff
There are 4 possible "boxes" to fill. In the first scenario you could have a single letter, or a word that is 12 characters long. ONLY you in theory know that.
In the second scenario you only have 255 characters most of which are invalid or not actual characters you can type (think ASCII).
So the first option only asking for 4 words offers a user HUGE amounts of entropy with LITTLE memory required. Another example:
Morgans Cat Bought Ricecakes
What are the odds you would forget that if you made it up? And better. What are the odds someone would guess that?
Using ASCII we get:
Hex: 4d 6f 72 67 61 6e 73 20 43 61 74 20 42 6f 75 67 68 74 20 52 69 63 65 63 61 6b 65 73
Binary: 1001101011011110111001001100111011000010110111001110011001000000100001101100001011101000010000001000010011011110111010101100111011010000111010000100000010100100110100101100011011001010110001101100001011010110110010101110011
Decimal: 8,154,893,049,812,103,173,157,262,565,599,567,087,077,694,151,135,108,193,841,698,268,531
Versus
mCbR
Which is the first letter of each with some capitalized and others not. Let's compare:
Hex: 6d 43 62 52
Binary: 1101101010000110110001001010010
Decimal: 18,33,132,626
See the difference? We don't even need to use math (entropy) to realize that the ability for us to remember both is just as easy yet the security is INSANELY different. Words should replace single characters. Remember 1 character is 8 byte and the more of them we can remember in our head (words) the more secure we can make passwords we can still remember!
Science!!! Digital science albeit but science none the less
Yes simple stuff but most people don't understand entropy. The study of random ;)